{"id":2219,"date":"2023-10-02T11:01:06","date_gmt":"2023-10-02T11:01:06","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2219"},"modified":"2023-10-02T11:02:26","modified_gmt":"2023-10-02T11:02:26","slug":"week-10-ss1-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-10-ss1-second-term-mathematics-notes\/","title":{"rendered":"Week 10 &#8211; SS1 Second Term Mathematics Notes"},"content":{"rendered":"<p><strong>WEEK TEN<br \/>\n<\/strong><strong>TOPIC: LOGIC<br \/>\n<\/strong><strong>CONTENT<br \/>\n<\/strong><\/p>\n<ul>\n<li>\n<div>Simple true and false statements\n<\/div>\n<\/li>\n<li>\n<div>Negative and contra positive of simple statement.\n<\/div>\n<\/li>\n<li>\n<div>Antecedents, consequence and conditional statement (implication)\n<\/div>\n<\/li>\n<\/ul>\n<p>\u00a0<strong>LOGICAL STATEMENTS<br \/>\n<\/strong>A logical statement is a declaration verbal or written that is either true or   false but not both.<br \/>\nA true statement has a truth value T<br \/>\nA false statement has a truth value F<br \/>\nLogical statements are denoted by letters p, q, r \u2026\u2026<br \/>\nQuestions, exclamations, commands and expression of feelings are not logical statements.<br \/>\nEx: 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\u00a0\u00a0\u00a0\u00a0(Not statement)\n<\/li>\n<li>If I run I shall not be late \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Statement)\n<\/li>\n<li>Japanese are hardworking people\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Statement)\n<\/li>\n<li>What a lovely man!\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Not statement)\n<\/li>\n<li>The earth is conical in shape\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Statement)\n<\/li>\n<li>If I think of my family\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Not statement)\n<\/li>\n<li>Take the pencil away\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Not statement)\n<\/li>\n<\/ol>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>State which of the statements is a logical statement<br \/>\n1.\u00a0\u00a0\u00a0\u00a0Caesar was great leader<br \/>\n2.\u00a0\u00a0\u00a0\u00a0Oh Mansa Musa, you are wonderful!<br \/>\n3.\u00a0\u00a0\u00a0\u00a0Is he a serious teacher at all?<br \/>\n4.\u00a0\u00a0\u00a0\u00a0If 6 is an odd number, then 3 + 5 = 10<br \/>\n5.\u00a0\u00a0\u00a0\u00a0Stop talking to the boy<br \/>\n6.\u00a0\u00a0\u00a0\u00a0The Broking House In Ibadan is a magnificent building<br \/>\n\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0<strong>SOLUTION<br \/>\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0A Logical statement<br \/>\n2.\u00a0\u00a0\u00a0\u00a0Not a logical statement (Exclamation)<br \/>\n3.\u00a0\u00a0\u00a0\u00a0Not a logical statement (Question)<br \/>\n4.\u00a0\u00a0\u00a0\u00a0A logical statement<br \/>\n5.\u00a0\u00a0\u00a0\u00a0Not a logical statement (command)<br \/>\n6.\u00a0\u00a0\u00a0\u00a0A logical statement<br \/>\n\u00a0\u00a0\u00a0\u00a0Reading Assignment: Further Maths Project Ex 9a Q 1&amp;2                      <\/p>\n<p>\u00a0<strong>NEGATION<br \/>\n<\/strong>Given a statement p, the negation of p written ~p is the statement &#8216;it is false that p&#8221; or \u00a0\u00a0\u00a0\u00a0&#8220;not p&#8221;<br \/>\n\u00a0\u00a0\u00a0\u00a0If P is true,<sup>(T)  <\/sup>~p is false<sup>(F)<\/sup>and if P is false<sup>(F)<\/sup>~p is true<sup>(T)<\/sup> .<br \/>\n\u00a0\u00a0\u00a0\u00a0The relationship between P and ~p is shown in a table called a truth table<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1101_Week10SS1S1.png\" alt=\"\"\/>                                     P        ~p<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0        T          F<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0F         T<br \/>\nEx I: Let P be the statement &#8216;Nigeria is a rich country&#8217; then ~p 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>\u00a0Ex II: Let r be the statement 3 + 4 = 8 then ~p is the statement 3 + 4 \u00b9 8<br \/>\nEx III: Let q be the statement &#8216;isosceles triangle are equiangular&#8217; then ~q 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<br \/>\n<strong>EVALUATION<br \/>\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0Write the negation each of the following statements.<br \/>\n\u00a0\u00a0\u00a0\u00a01.\u00a0\u00a0\u00a0\u00a0It is very hot in the tropics.<br \/>\n\u00a0\u00a0\u00a0\u00a02.\u00a0\u00a0\u00a0\u00a0He is a handsome man.<br \/>\n\u00a0\u00a0\u00a0\u00a03.\u00a0\u00a0\u00a0\u00a0The football captain scored the first goal.<br \/>\n\u00a0\u00a0\u00a0\u00a04.\u00a0\u00a0\u00a0\u00a0Short cuts are dangerous.<br \/>\n2.\u00a0\u00a0\u00a0\u00a0Write the negation of each of the following avoiding the word &#8216;not&#8217; as much as possible.<\/p>\n<ol>\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<br \/>\n<\/strong>Further maths projects Ex. 9a Q 3 \u2013 7.<br \/>\n\u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>CONDITIONAL STATEMENTS<br \/>\n<\/strong>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 combining the two statements is &#8216;If Femi is a brilliant \u00a0\u00a0\u00a0\u00a0student then Femi passed the test&#8217; or &#8216;If q then r&#8217;<\/p>\n<p>\u00a0The statement &#8216;If q then r&#8217; is a combination of two simple statements q and r. It is called a compound statement.<br \/>\nSymbolically, the compound statement can be written as follows: &#8216;If q then r&#8217; as q \u00de r<br \/>\n\u00a0\u00a0\u00a0\u00a0The statement q \u00de r is real as<br \/>\n\u00a0\u00a0\u00a0\u00a0q implies r or<br \/>\n\u00a0\u00a0\u00a0\u00a0if q then r or<br \/>\n\u00a0\u00a0\u00a0\u00a0q if r<br \/>\n\u00a0\u00a0\u00a0\u00a0The symbol \u00de is an operation. In the compound statement q \u00de r, the statement q is called \u00a0\u00a0\u00a0\u00a0the antecedent while the sub statement r is called the consequence of q \u00de r.<br \/>\n\u00a0\u00a0\u00a0\u00a0The truth or falsity table for q \u00de r is shown below.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1101_Week10SS1S2.png\" alt=\"\"\/><br \/>\n\t                                                 q            r        q \u00de r<br \/>\n                                                  T           TT<\/p>\n<p>\u00a0                                                  T           F        F<\/p>\n<p>\u00a0                                                  F           T        T<\/p>\n<p>\u00a0                                                  F           F        T<\/p>\n<p>\u00a0Ex: 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\u00a0\u00a0\u00a0\u00a0\u00a0Consider the statements.<br \/>\na.\u00a0\u00a0\u00a0\u00a0If I am a male then the sun will rise<br \/>\nb.\u00a0\u00a0\u00a0\u00a0If I am a male then the sun will not rise<br \/>\nc.\u00a0\u00a0\u00a0\u00a0If I am not a male then the sun will rise<br \/>\nd.\u00a0\u00a0\u00a0\u00a0If I am not a male then the sun will not rise<br \/>\nThe statement (a), (c) and (d) are all true but b is not true because the antecedent is true and the consequent is false.<\/p>\n<p>\u00a0<strong>CONVERSE STATEMENT<\/strong>: The statement q \u00de p is called the converse of the statement  p\u00de q. e.g. Let p be the statement &#8216;a triangle is equiangular&#8217; and q the statement &#8216;a triangle is equilateral&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0The State p \u00de q means if a triangle is equiangular then it is equilateral.<br \/>\n\u00a0\u00a0\u00a0\u00a0The statement q \u00de p means if a triangle is equilateral then it is equiangular.<\/p>\n<p>\u00a0<strong>INVERSE STATEMENT<\/strong>: This statement ~p \u00de~ q is called the inverse of the statement                \u00a0\u00a0\u00a0\u00a0p \u00de q. If p is the statement &#8216;a triangle is equiangular and q is the statement &#8216;a triangle is \u00a0\u00a0\u00a0\u00a0equilateral&#8217; the statement~p \u00de~ q is the statement &#8216;if a triangle is not equiangular then it \u00a0\u00a0\u00a0\u00a0is not equilateral&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>CONTRAPOSITIVE STATEMENT<\/strong>: The statement ~q \u00de~ p is called the contrapositive statement of p \u00de q.<br \/>\n\u00a0\u00a0\u00a0\u00a0If p is the statement &#8216;I can swim&#8217; and q is the statement &#8216;I will win&#8217; then the statement                \u00a0\u00a0\u00a0\u00a0~q \u00de~ p is the statement &#8216;If I cannot swim then I cannot win&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>EVALUATION<br \/>\n<\/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.<br \/>\n(i)\u00a0\u00a0\u00a0\u00a0If it rains sufficiently then the harvest will be good.<br \/>\n(ii)\u00a0\u00a0\u00a0\u00a0If it doesn&#8217;t rain sufficiently then the harvest will be poor.<br \/>\n(iii)\u00a0\u00a0\u00a0\u00a0If the harvest is poor then it doesn&#8217;t rain sufficiently.<br \/>\n(iv)\u00a0\u00a0\u00a0\u00a0It doesn&#8217;t rain sufficiently.<br \/>\n(v)\u00a0\u00a0\u00a0\u00a0If it doesn&#8217;t rain sufficiently then the harvest will be good.<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<strong>IDENTIFICATION OF ANTICEDENCE AND CONSEQUENCE OF SIMPLE STATEMENTS.<br \/>\n<\/strong>1.\u00a0\u00a0\u00a0\u00a0Biconditional statements<br \/>\n2.\u00a0\u00a0\u00a0\u00a0The Chain Rule<br \/>\n 1. <strong>BICONDITIONAL STATEMENTS :<\/strong>If p and q are statements such that p \u00de q and q \u00de p are valid, then p and q imply each other or p is equivalent to q and we write p \u00db q. The statement p \u00db 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<\/strong>\u00a0\u00a0\u00a0\u00a0p \u00db q could be read as<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0q is equivalent to p or<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0q if and only if p or<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0p if and only if q or<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if p then q and if q then p<br \/>\n\u00a0\u00a0\u00a0\u00a0<br \/>\n\t\tThe truth or falsity of p \u00db q is shown below.<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>P<\/td>\n<td>q<\/td>\n<td>p \u00db 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\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\nA biconditional 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 \u00a0\u00a0\u00a0\u00a0&#8216;a polygon is regular&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0p \u00de q is the statement &#8216;if the interior angles of a polygon are equal then the polygon is \u00a0\u00a0\u00a0\u00a0regular&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0q \u00de  p is the statement &#8216;if a polygon is regular then the interior angles of the polygon are \u00a0\u00a0\u00a0\u00a0equal&#8217;.<br \/>\n\u00a0\u00a0\u00a0\u00a0p \u00de q and q \u00de p<br \/>\n\u00a0\u00a0\u00a0\u00a0p \u00db q<br \/>\n\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;<br \/>\n\u00a0\u00a0\u00a0\u00a0                Let q be the statement &#8216;Mary is beautiful&#8217;<br \/>\n\u00a0\u00a0\u00a0\u00a0Consider these statements.<br \/>\na.\u00a0\u00a0\u00a0\u00a0Mary is a model if and only if she is beautiful.<br \/>\nb.\u00a0\u00a0\u00a0\u00a0Mary is a model if and only if she is ugly.<br \/>\nc.\u00a0\u00a0\u00a0\u00a0Mary is not a model if and only if she is beautiful.<br \/>\nd.\u00a0\u00a0\u00a0\u00a0Mary is not a model if and only if she is ugly.<br \/>\nStatements a and d are true because the sub-statements have the same truth value. Statements \u00a0\u00a0\u00a0\u00a0b 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 \u00de q and q \u00de r.<strong><br \/>\n\t\t<\/strong>Ex I:     Consider the arguments<br \/>\nPremise\u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub>: If a student works very hard, he passes his examination<br \/>\nPremise \u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub>: If a student passes his examination he is awarded a certificate.<br \/>\nConclusion\u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub>: If a student works very hard, he is awarded a certificate.<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0SOLUTION<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Let p be the statement &#8220;a student works very hard&#8221;<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Let q be the statement &#8220;a student passes his examination&#8221;<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Let r be the statement &#8220;a student is awarded a certificate&#8221;<br \/>\n\u00a0\u00a0\u00a0\u00a0&#8216;The argument has the following structural form.<br \/>\n\u00a0\u00a0\u00a0\u00a0  p \u00de q and q \u00de r  \\ p \u00de r<br \/>\n\u00a0\u00a0\u00a0\u00a0This argument follows the chain rule link hence it is said to be valid.<br \/>\n\u00a0\u00a0\u00a0\u00a0Ex II: \u00a0\u00a0\u00a0\u00a0Consider the arguments<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub>: Soldiers are disciplined<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub>: Good leaders are disciplined men<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub>: Soldiers are good leaders.<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0SOLUTION<br \/>\n<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;<br \/>\n\u00a0\u00a0\u00a0\u00a0The argument has the following structural form.<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>1<\/sub> : p \u00de q<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>2<\/sub> : r  \u00de q<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0T<sub>3<\/sub> : p \u00de 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<br \/>\n<strong>EVALUATION<br \/>\n<\/strong>Give an outline of the structural form of the following arguments and state whether or notit is valid.<br \/>\nT<sub>1<\/sub> : It is necessary to stay healthy in order to live long.<br \/>\nT<sub>2<\/sub> : It is necessary to eat balanced diet in order to stay healthy.<br \/>\nT<sub>3<\/sub> : It is necessary to eat balanced diet in order to live long.<\/p>\n<p>\u00a0<strong>GENERAL EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div><strong>Determine which of the following are true and which are false. <\/strong>\n\t\t\t<\/div>\n<ol>\n<li>(5 = 8 &#8211; 2)  (4 + 7 = 11)\n<\/li>\n<li>(15 &gt; 10) (0 &gt; &#8211; 12)\n<\/li>\n<li>(3, 4, 5) is a Pythagorean triples or (9, 12, 15) is a Pythagorean triples.\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Write the converse and the inverse of the following implications:\n<\/div>\n<ol>\n<li>If the bus has a driver, then the bus can carry the passengers.\n<\/li>\n<li>M  N\n<\/li>\n<li>A\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>WABP Essential Mathematics page 189 \u2013 190 exercise 14.3 no 5 \u2013 10<\/p>\n<p>\u00a0<strong>WEEKEND ASSIGNMENT<\/strong><br \/>\n\tP is the statement &#8216;Ayo has determination and q is the statement &#8216;Ayo will succed&#8217;. Use this information to answer these questions.<br \/>\nWhich of these symbols represent these statements?<br \/>\n1.\u00a0\u00a0\u00a0\u00a0Ayo has no determination.<br \/>\nA.\u00a0\u00a0\u00a0\u00a0P \u00de q      B.   ~ p \u00de q          C.      ~ p<br \/>\n2. \u00a0\u00a0\u00a0\u00a0If Ayo has no determination then he won&#8217;t succeed.<br \/>\nA.\u00a0\u00a0\u00a0\u00a0~p \u00de~ q     B. p \u00de~ q        C.  p \u00de q        D.   p \u00de~ q<br \/>\n3.\u00a0\u00a0\u00a0\u00a0If Ayo won&#8217;t succeed then he has no determination.<br \/>\nA.\u00a0\u00a0\u00a0\u00a0~q \u00de p      B.    ~q \u00de~q        C.   ~q \u00de p      D. q \u00de p<br \/>\n4.\u00a0\u00a0\u00a0\u00a0If Ayo has determination then he will succeed.<br \/>\nA.\u00a0\u00a0\u00a0\u00a0~p \u00de q     B. ~p \u00de~ q       C.  ~q \u00de~ p     D. p \u00de q<br \/>\n5.\u00a0\u00a0\u00a0\u00a0If Ayo has no determination then he will succeed.<br \/>\nA.\u00a0\u00a0\u00a0\u00a0~p \u00de q     B.  ~q \u00de~ p       C. ~p      D. ~p \u00de~ q<\/p>\n<p>\u00a0<strong>THEORY<br \/>\n<\/strong>1. Write down the inverse, converse and contrapositive of each of these statements.<br \/>\n(i)\u00a0\u00a0\u00a0\u00a0If the bank workers work hard they will be adequately compensated.<br \/>\n(ii)\u00a0\u00a0\u00a0\u00a0If he is humble and prayerful, he will meet with God&#8217;s favour.<br \/>\n(iii)\u00a0\u00a0\u00a0\u00a0If he sets a good example, he will get a good followership.<br \/>\n2. Find the truth value of these statements.<br \/>\na.\u00a0\u00a0\u00a0\u00a0If 11 &gt; 8 then -1&lt; -8<br \/>\nb.\u00a0\u00a0\u00a0\u00a0If 3 + 4 \u00b9 10 then 2 + 3 \u00b9 5 <strong><br \/>\n\t\t<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>WEEK TEN TOPIC: LOGIC CONTENT Simple true and false statements Negative and contra positive of&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,190],"tags":[],"class_list":["post-2219","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-general-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2219","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=2219"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2219\/revisions"}],"predecessor-version":[{"id":2220,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2219\/revisions\/2220"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}