{"id":2179,"date":"2023-10-02T10:34:02","date_gmt":"2023-10-02T10:34:02","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2179"},"modified":"2023-10-02T10:35:05","modified_gmt":"2023-10-02T10:35:05","slug":"week-9-ss1-second-term-further-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-9-ss1-second-term-further-mathematics-notes\/","title":{"rendered":"Week 9 &#8211; SS1 Second Term Further Mathematics Notes"},"content":{"rendered":"<h3>WEEK  NINE \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0DATE\u2026\u2026\u2026\u2026\u2026 TOPIC: LOGIC CONTENT<br \/>\n<\/h3>\n<ul>\n<li>Logical Statements \u2756 \u00a0\u00a0\u00a0\u00a0Negations\n<\/li>\n<li>Conditional statements and bi-conditional statements.\n<\/li>\n<li>Identification of Antecedence &amp; Consequence of Simple Statement\n<\/li>\n<\/ul>\n<p> \u00a0\u00a0\u00a0\u00a0 <\/p>\n<h3> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0LOGICAL STATEMENTS<br \/>\n<\/h3>\n<p>A logical statement is a declaration verbal or written that is either true or   false but not both.<br \/>\n \u00a0\u00a0\u00a0\u00a0A true statement has a truth value T<br \/>\n \u00a0\u00a0\u00a0\u00a0A false statement has a truth value F<br \/>\n \u00a0\u00a0\u00a0\u00a0Logical statements are denoted by letters p, q, r \u2026\u2026<br \/>\n \u00a0\u00a0\u00a0\u00a0Questions, exclamations, commands and expression of feelings are not logical statements.<br \/>\n \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>Example<\/strong>: Which of the following are logical statements? <\/p>\n<ol>\n<li>Nigeria is an African country \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Statement)\n<\/li>\n<li>Who is he? \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Not statement) iii. \u00a0\u00a0\u00a0\u00a0If I run I shall not be late  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 (Statement) iv. \u00a0\u00a0\u00a0\u00a0Japanese are hardworking people \u00a0\u00a0\u00a0\u00a0 (Statement)\n<\/li>\n<\/ol>\n<p>v. \u00a0\u00a0\u00a0\u00a0What a lovely man! \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Not statement) vi. \u00a0\u00a0\u00a0\u00a0The earth is conical in shape \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Statement) vii. \u00a0\u00a0\u00a0\u00a0If I think of my family \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Not statement) viii. \u00a0\u00a0\u00a0\u00a0Take the pencil away \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(Not statement) <\/p>\n<p>\u00a0<\/p>\n<h4> \u00a0\u00a0\u00a0\u00a0Evaluation<br \/>\n<\/h4>\n<p> \u00a0\u00a0\u00a0\u00a0State which of the statements is a logical statement <\/p>\n<ol>\n<li>Caesar was great leader\n<\/li>\n<li>Oh Mansa Musa, you are wonderful!\n<\/li>\n<li>Is he a serious teacher at all?\n<\/li>\n<li>If 6 is an odd number, then 3 + 5 = 10\n<\/li>\n<li>Stop talking to the boy\n<\/li>\n<li>The Broking House In Ibadan is a magnificent building\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<\/p>\n<h3>NEGATION<br \/>\n<\/h3>\n<p> Given a statement p, the negation of p written \uf07ep is the statement &#8216;it is false that p&#8221; or &#8220;not p&#8221;  If P is true (T), \uf07ep is false(F)and if P is false(F) \uf07ep is true(T) .<br \/>\n \u00a0\u00a0\u00a0\u00a0The relationship between P and \uf07ep is shown in a table called a truth table<br \/>\n \u00a0\u00a0\u00a0\u00a0 <\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>\uf07ep<\/td>\n<td> \u00a0<\/td>\n<\/tr>\n<tr>\n<td>T      <\/td>\n<td>     F <\/td>\n<\/tr>\n<tr>\n<td>F     <\/td>\n<td>     T <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>                                             P<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0 \u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Example I: Let P be the statement &#8216;Nigeria is a rich country&#8217; then \uf07ep is the statement &#8216;It is false that Nigeria is a rich country or &#8216;Nigeria is not a rich country&#8217; <\/p>\n<p>\u00a0Example II: Let r be the statement 3 + 4 = 8 then \uf07ep is the statement 3 + 4 \uf0b9 8<br \/>\nExample III: Let q be the statement &#8216;isosceles triangle are equiangular&#8217; then \uf07eq is the statement &#8216;it is false that isosceles triangles are equiangular or &#8216;isosceles triangle are not equiangular&#8217;.<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 <\/p>\n<h4>Evaluation<br \/>\n<\/h4>\n<ol>\n<li>\n<div>Write the negation each of the following statements.\n<\/div>\n<ol>\n<li>It is very hot in the tropics.\n<\/li>\n<li>He is a handsome man.\n<\/li>\n<li>The football captain scored the first goal.\n<\/li>\n<li>Short cuts are dangerous.\n<\/li>\n<\/ol>\n<\/li>\n<li>Write the negation of each of the following avoiding the word &#8216;not&#8217; as much as possible.\n<\/li>\n<li>He was present in school yesterday.\n<\/li>\n<li>His friend is younger than my brother.\n<\/li>\n<li>She is the shortest girl in the class.\n<\/li>\n<li>He obtained the least mark in the examination.\n<\/li>\n<\/ol>\n<p> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>Reading Assignment: Further Maths projects Ex. 9a Q 3 \u2013 7. <\/strong><br \/>\n\t \u00a0\u00a0\u00a0\u00a0 <\/p>\n<h3> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0CONDITIONAL STATEMENTS<br \/>\n<\/h3>\n<p>Let q stand for the statement &#8216;Femi is a brilliant student&#8217; and r stand for the statement &#8216;Femi passed the test&#8217;. One way of combing the two statement is &#8216;If Femi is a brilliant  \u00a0\u00a0\u00a0\u00a0student then Femi passed the test&#8217; or &#8216;If q then r&#8217;<br \/>\n \u00a0\u00a0\u00a0\u00a0The student &#8216;If q then r&#8217; is a combination of two simple statements q and r. It is called a compound statement.<br \/>\n \u00a0\u00a0\u00a0\u00a0Symbolically, the compound statement can be written as follows: &#8216;If q then r&#8217; as q \uf0de r<br \/>\n \u00a0\u00a0\u00a0\u00a0The statement q \uf0de r is real as<br \/>\n \u00a0\u00a0\u00a0\u00a0q implies r or   \u00a0\u00a0\u00a0\u00a0if q then r or q if r<br \/>\n \u00a0\u00a0\u00a0\u00a0The symbol \uf0de is an operation. In the compound statement q \uf0de r, the statement q is called the  antecedent while the sub statement r is called the consequence of q \uf0de r.  \u00a0\u00a0\u00a0\u00a0The truth or falsity table for q \uf0de r is shown below. <\/p>\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>q            r              q <\/td>\n<td>\uf0de r    <\/td>\n<\/tr>\n<tr>\n<td>T           TT<\/td>\n<td> \u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>T           F                F<\/td>\n<td> \u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>F           T                T<\/td>\n<td> \u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0  F           FT <\/p>\n<p>\u00a0<strong>Example<\/strong>: If q is the statement &#8216;I am a male&#8217; and r is the statement &#8216;The sun will rise&#8217;<br \/>\n \u00a0\u00a0\u00a0\u00a0Consider the statements. <\/p>\n<ol>\n<li>If I am a male then the sun will rise\n<\/li>\n<\/ol>\n<ol>\n<li>If I am a male then the sun will not rise\n<\/li>\n<li>If I am not a male then the sun will rise\n<\/li>\n<li>If I am not a male then the sun will not rise\n<\/li>\n<\/ol>\n<p>The statement (a), (c) and (d) are all true but b is not true b and c the antecedent is true and the consequent is false. <\/p>\n<p>\u00a0<strong>CONVERSE STATEMENT<\/strong>: The statement q \uf0de p is called the converse of the statement p \uf0dep. e.g. Let p be the statement &#8216;a triangle is equiangular&#8217; and q the statement &#8216;a triangle is equilateral&#8217;.  \u00a0\u00a0\u00a0\u00a0The State p \uf0dep means if a triangle is equiangular then u is equilateral.<br \/>\n \u00a0\u00a0\u00a0\u00a0The statement q \uf0de p means if a triangle is equilateral then u is equiangular. <\/p>\n<p>\u00a0<strong>INVERSE STATEMENT<\/strong>: This statement \uf07ep \uf0de\uf07e q is called the inverse of the statement p \uf0de q.  If p is the statement &#8216;a triangle is equiangular and q is the statement &#8216;a triangle is equilateral&#8217;   the statement \uf07ep \uf0de\uf07e q is the statement &#8216;if a triangle is not equiangular then it is not equilateral&#8217;.<br \/>\n \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>CONTRAPOSITIVE STATEMENTS<\/strong>: The statement \uf07eq \uf0de\uf07e p is called the contrapositive statement of p \uf0de q. If p is the statement &#8216;I can swim&#8217; and q is the statement &#8216;I will win&#8217; then the statement \uf07eq \uf0de\uf07e p is the statement &#8216;If I cannot swim then I cannot win&#8217;.<br \/>\n \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>Evaluation <\/strong>If p is the statement &#8216;it rains sufficiently&#8217; and q the statement &#8216;the harvest will be good&#8217; write the symbol of these statements. <\/p>\n<ol>\n<li>If it rains sufficiently then the harvest will be good.\n<\/li>\n<li>If it doesn&#8217;t rain sufficiently then it doesn&#8217;t\n<\/li>\n<li>If the harvest is poor then it doesn&#8217;t rain sufficiently.\n<\/li>\n<li>It doesn&#8217;t rain sufficiently.\n<\/li>\n<li>If it doesn&#8217;t rain sufficiently then the harvest will be good.\n<\/li>\n<\/ol>\n<p> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>IDENTIFICATION OF ANTICEDENCE AND CONSEQUENCE OF SIMPLE STATEMENTS. <\/strong><\/p>\n<ol>\n<li>Bi-conditional statements\n<\/li>\n<li>The Chain Rule\n<\/li>\n<\/ol>\n<p>\u00a0 1. <strong>BICONDITIONAL STATEMENTS : <\/strong>If p and q are statements such that p \uf0de q and q \uf0de p are valid, then p and q        imply each other or p is equivalent to q and we write p \uf0db q. The statement p \uf0db q is called a biconditional        statement of p and q and the statement p and q are equivalent to each other.<strong><br \/>\n\t\t\t<\/strong><\/p>\n<ol>\n<li>\uf0db q could be read as\n<\/li>\n<li>is equivalent to p or  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0q if and only if p or  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0p if and only if q or  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0if p then q and if q then p\n<\/li>\n<\/ol>\n<p>The truth or falsity of p \uf0db q is shown below. <\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>P <\/td>\n<td>Q <\/td>\n<td>P \u21d4 q <\/td>\n<\/tr>\n<tr>\n<td>T <\/td>\n<td>T <\/td>\n<td>T <\/td>\n<\/tr>\n<tr>\n<td>T <\/td>\n<td>F <\/td>\n<td>F <\/td>\n<\/tr>\n<tr>\n<td>F <\/td>\n<td>T <\/td>\n<td>F <\/td>\n<\/tr>\n<tr>\n<td>F <\/td>\n<td>F <\/td>\n<td>T <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>  \u00a0\u00a0\u00a0\u00a0<br \/>\nA bi-conditional statement is true when two sub-statements have the same truth value.<br \/>\ne.g. If p is the statement &#8216;the interior angle of a polygon are equal&#8217; and q is the statement &#8216;a polygon is regular&#8217;.  \u00a0\u00a0\u00a0\u00a0p \uf0de q is the statement &#8216;if the interior angles of a polygon are equal then the polygon is regular&#8217;.  \u00a0\u00a0\u00a0\u00a0q \uf0de  p is the statement &#8216;if a polygon is regular then the interior angles of the polygon are equal&#8217;.  \u00a0\u00a0\u00a0\u00a0p \uf0de q and q \uf0de p   \u00a0\u00a0\u00a0\u00a0p \uf0db q  \u00a0\u00a0\u00a0\u00a0p and q are equivalent to each other.<br \/>\n \u00a0\u00a0\u00a0\u00a0Examples: Let p be the statement &#8216;Mary is a model&#8217;  \u00a0\u00a0\u00a0\u00a0                   Let q be the statement &#8216;Mary is beautiful&#8217;        Consider these statements. <\/p>\n<ol>\n<li>Mary is a model if and only if she is beautiful.\n<\/li>\n<li>Mary is a model if and only if she is ugly.\n<\/li>\n<li>Mary is not a model if and only if she is beautiful.\n<\/li>\n<li>Mary is not a model if and only if she is ugly.\n<\/li>\n<\/ol>\n<p>Statements a and d are true b and c the sub-statements have the same truth value. Statements b and c are false because the sub-statements have different truth values.<br \/>\n \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>2. THE CHAIN RULE: <\/strong>If p, q and r, are three statements such that p \uf0de q and q \uf0de r.<strong><br \/>\n\t\t\t<\/strong><\/p>\n<p>\u00a0Example I:     Consider the arguments <\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Premise <\/td>\n<td>T<sub>1<\/sub>: If a student works very hard, he passes his examination <\/td>\n<\/tr>\n<tr>\n<td>Premise  <\/td>\n<td>T<sub>2<\/sub>: If a student passes his examination he is awarded a certificate. <\/td>\n<\/tr>\n<tr>\n<td>Conclusion<br \/>\n \u00a0<\/td>\n<td>T<sub>3<\/sub>: If a student works very hard, he is awarded a certificate. <\/td>\n<\/tr>\n<tr>\n<td> \u00a0\u00a0\u00a0\u00a0 <\/td>\n<td><strong>SOLUTION <\/strong><\/td>\n<\/tr>\n<tr>\n<td> \u00a0\u00a0\u00a0\u00a0 <\/td>\n<td>Let p be the statement &#8220;a student works very hard&#8221; <\/td>\n<\/tr>\n<tr>\n<td> \u00a0\u00a0\u00a0\u00a0 <\/td>\n<td>Let q be the statement &#8220;a student passes his examination&#8221; <\/td>\n<\/tr>\n<tr>\n<td> \u00a0\u00a0\u00a0\u00a0 <\/td>\n<td>Let r be the statement &#8220;a student is awarded a certificate&#8221; <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> \u00a0\u00a0\u00a0\u00a0&#8216;The argument has the following structural form.<br \/>\n \u00a0\u00a0\u00a0\u00a0  p \uf0de q and q \uf0de r  \uf05c p \uf0de r<br \/>\n \u00a0\u00a0\u00a0\u00a0This argument follows the chain rule link hence u is said to be valid.<br \/>\n \u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>Example II<\/strong>:  Consider the arguments<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub>: Soldiers are disciplined  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub>: Good leaders are disciplined men  \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub>: Soldiers are good leaders. <\/p>\n<p>\u00a0<\/p>\n<h3> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0SOLUTION<br \/>\n<\/h3>\n<p><strong> \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0<\/strong>Let p be the statement &#8216;X is a seller&#8217;<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0Let q be the statement &#8216;X is a disciplined man&#8217;<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0Let r be the statement &#8216;X is a good leader&#8217;  \u00a0\u00a0\u00a0\u00a0The argument has the following structural form.<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub> : p \uf0de q<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub> : r  \uf0de q<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub> : p \uf0de r<br \/>\n \u00a0\u00a0\u00a0\u00a0The argument does not follow the format of the chain rule, hence it is not valid.<br \/>\n \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 <\/p>\n<h4>Evaluation I<br \/>\n<\/h4>\n<p> \u00a0\u00a0\u00a0\u00a0Give an outline of the structural form of the following arguments and state whether or not it is valid.<br \/>\n \u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub> : It is necessary to stay healthy in order to live long.<br \/>\n \u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub> : It is necessary to eat balanced diet in order to stay healthy.  \u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub> : It is necessary to eat balanced diet in order to lives long. <\/p>\n<p>\u00a0<\/p>\n<h4>Evaluation II<br \/>\n<\/h4>\n<ol>\n<li>Let P be the statement : &#8220;He is funny&#8221; and q be the statement : &#8220;He is serious&#8221;. Write each of the following in simple English (i) p v q (ii) p \u02c4 q (iii) p\u02c4 ~q (iv) ~pv~q\n<\/li>\n<li>If p and q represent two statements &#8220;he is good in physics&#8221; and &#8220;he is good in mathematics&#8221; respectively. write the following in symbolic form; &#8220;he is good in physics if and only if he is good in mathematics&#8221;.\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<h4>General Evaluation<br \/>\n<\/h4>\n<ol>\n<li>\n<div>Find the truth value of these statements.\n<\/div>\n<ol>\n<li>If 11 \uf03e 8 then -1\uf03c -8\n<\/li>\n<li>If 3 + 4 \uf0b9 10 then 2 + 3 \uf0b9 5\n<\/li>\n<\/ol>\n<\/li>\n<li>Find the values of x satisfying 2<sup>3x + 1 <\/sup>  &#8211;  3 (2<sup>2x<\/sup>) + 2<sup>x + 1<\/sup> = 2<sup>x<\/sup>\n\t\t<\/li>\n<li>Solve the equation 3<sup>2x<\/sup> \u2013 30 (3<sup>x<\/sup>) + 81 = 0\n<\/li>\n<li>Solve the simultaneous equations 2x + y = 3;    4x<sup>2<\/sup> \u2013 y<sup>2<\/sup> + 2x + 3y = 16.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Reading Assignment: F\/Maths Project 1 pages 126 \u2013 130 Exercise 9b Q 2, 3 and 4 <\/strong><\/p>\n<p>\u00a0<br \/>\n\u00a0<\/p>\n<h3>WEEKEND ASSIGNMENT<br \/>\n<\/h3>\n<p>P is the statement &#8216;Ayo has determination and q is the statement &#8216;Ayo will succeed&#8217;. Use this information to answer these questions. Which of these symbols represent these statements?<br \/>\n1. \u00a0\u00a0\u00a0\u00a0Ayo has no determination.<br \/>\nA. \u00a0\u00a0\u00a0\u00a0P \uf0de q      B.   \uf07e p \uf0de q          C.      \uf07e p<br \/>\n2.  \u00a0\u00a0\u00a0\u00a0If Ayo has no determination then he won&#8217;t succeed.<br \/>\nA. \u00a0\u00a0\u00a0\u00a0\uf07ep \uf0de\uf07e q     B. p \uf0de\uf07e q        C.  p \uf0de q        D.   p \uf0de\uf07e q 3. \u00a0\u00a0\u00a0\u00a0If Ayo won&#8217;t succeed then he has no determination.<br \/>\nA. \u00a0\u00a0\u00a0\u00a0\uf07eq \uf0de p      B.    \uf07eq \uf0de\uf07eq        C.   \uf07eq \uf0de p      D. q \uf0de p<br \/>\n4. \u00a0\u00a0\u00a0\u00a0If Ayo has determination then he will succeed.<br \/>\nA. \u00a0\u00a0\u00a0\u00a0\uf07ep \uf0de q     B. \uf07ep \uf0de\uf07e q       C.  \uf07eq \uf0de\uf07e p     D. p \uf0de q<br \/>\n5. \u00a0\u00a0\u00a0\u00a0If Ayo has no determination then he will succeed. A. \u00a0\u00a0\u00a0\u00a0\uf07ep \uf0de q     B.  \uf07eq \uf0de\uf07e p       C. \uf07ep      D. \uf07ep \uf0de\uf07e q <\/p>\n<p>\u00a0<\/p>\n<h3>THEORY<br \/>\n<\/h3>\n<ol>\n<li>\n<div>Write down the inverse, converse and contrapositive of each of these statements.\n<\/div>\n<ol>\n<li>If the bank workers work hard they will be adequately compensated.\n<\/li>\n<li>If he is humble and prayerful, he will meet with God&#8217;s favour.     (iii) \u00a0\u00a0\u00a0\u00a0If he sets a good example, he will get a good followership.\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>\n<div>Consider the following statements P: Some dogs are tame    Q: All tame animals are small.         Which of the following is a valid conclusion from the above statements?\n<\/div>\n<ol>\n<li>All dogs are tame.  (ii) No dog is small.  (iii) All small animals are tame.  (iv) Some dogs are small.           (v) All tame animals are dogs.  \u00a0\u00a0\u00a0\u00a0\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><strong><br \/>\n\t\t\t<\/strong><br \/>\n\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>WEEK NINE \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0DATE\u2026\u2026\u2026\u2026\u2026 TOPIC: LOGIC CONTENT&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,188],"tags":[],"class_list":["post-2179","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-further-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2179"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2179\/revisions"}],"predecessor-version":[{"id":2180,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2179\/revisions\/2180"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}