{"id":2209,"date":"2023-10-02T10:55:49","date_gmt":"2023-10-02T10:55:49","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2209"},"modified":"2023-10-02T11:02:26","modified_gmt":"2023-10-02T11:02:26","slug":"week-4-ss1-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss1-second-term-mathematics-notes\/","title":{"rendered":"Week 4 &#8211; SS1 Second Term Mathematics Notes"},"content":{"rendered":"<p><strong>WEEK FOUR\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<\/strong><strong>TOPIC: IDEA OF SETS<br \/>\n<\/strong><strong>CONTENT<br \/>\n<\/strong><\/p>\n<ul>\n<li>\n<div>Notation of Set\n<\/div>\n<\/li>\n<li>\n<div>Types and Operation of Set.\n<\/div>\n<p>\u00a0<\/li>\n<\/ul>\n<p><strong>Definition of Set<br \/>\n<\/strong>A set is a welldefined collection of objects or elements having some common characteristic or properties. A set can be described by<\/p>\n<ol>\n<li>Listing of its elements\n<\/li>\n<li>Giving a property that clearly defines its element\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Notations used in set theory<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Elements of a set: the members of a set are called elementse.g list the elements of set\n<\/div>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1055_Week4SS1Se1.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1055_Week4SS1Se2.png\" alt=\"\"\/><br \/>\n\t\t\tA =     even numbers less than 10\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>n(A) means number of elements contained in a set\n<\/li>\n<li>E means &#8216;is an element of or &#8216;belongs to&#8217; e.g  6EA\n<\/li>\n<li><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1055_Week4SS1Se3.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1055_Week4SS1Se4.png\" alt=\"\"\/>E  means &#8216;is not an element of&#8217; or&#8217;did not belong to&#8217; e.g 5  A defined in number 1 above\n<\/li>\n<li>(:) means such that e.g B={X : 3 \u2264 X \u2264 10} means X is a member of B such that X is a number from 3 to 10\n<\/li>\n<li>Equal set: two sets are equal if they contain the same elements e.gIf S = {a,d,c,b} and P= {b,a,d,c,a,b}, then S=P repeated elements are counted once\n<\/li>\n<li>\n<div>\u0424 or { } means empty set or null set i.e A set which has no element e.g\n<\/div>\n<p> {secondary school student with age 3}\n<\/li>\n<li>means subset. B is a subset of A if all the elements of B are contained in A e.gIf A ={1,2,3,4} and B = {1,2,3} then B is a subset of A i.e B \u2282A\n<\/li>\n<li>U means union: all elements belonging to two or more given sets. A U B means list all elements in A and B e.g.If A ={2,4,6,8,10}  and B = {1,3,5,7,9}  then A U B ={1,2,3,4,5,6,7,8,9,10}\n<\/li>\n<li>\u2229 means intersection i.e elements common to 2 or more sets e.gA ={1,2,3,4,5,6} and B ={1,3,5,7,9} then A\u2229B = {1,3,5}\n<\/li>\n<li>\u01b2 and E means universal set i.e a large set containing all the original given set i.e A set containing all elements in a given problem or situations under consideration\n<\/li>\n<li>\n<div>Complement of a set i.e A<sup>|<\/sup>. A<sup>|<\/sup> means &#8216;A complement&#8217; and it is the set which contains elements that are not elements of set A but are in the universal set under consideration. E.gIf E ={shoes and sock} and A={socks}, then A<sup>|<\/sup> ={shoes}\n<\/div>\n<p>\u00a0<\/li>\n<\/ol>\n<p><strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>State the elements in the given set below: Y= {Y: Y E integer -4\u2264Y\u2264 3}\n<\/li>\n<li>\n<div>Let E={x\u00f710&lt;x&lt; 20}         P= {prime numbers}       Q= {odd numbers}\n<\/div>\n<p>Where P and Q are subsets of E\n<\/li>\n<li>List all elements of set P      (b) What is n(P)?      (c) List all elements of set Q     (d) List the elements of P<sup>|<\/sup>\n\t\t<\/li>\n<li><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1055_Week4SS1Se5.png\" alt=\"\"\/>Make each of the following statements true by writing E or E in place of *\n<\/li>\n<li>17 * 1,2,3,\u2026\u2026\u20267, 8,9 {        }\n<\/li>\n<li>11 * 1,3,5,7\u2026\u2026\u2026\u2026. 19 {        }\n<\/li>\n<\/ol>\n<p><strong>TYPES OF SETS<br \/>\n<\/strong><\/p>\n<ol>\n<li>Universal set: A larger set containing all other sets under consideration i.e a set of students in a school\n<\/li>\n<li>Finite set: is a set which contains a fixed number of elements. This means that a finite set has an end. E.g B={1,2,3,4,5}\n<\/li>\n<li>Infinite set: is a set which has unending number of elements or which has an infinite number of elements. An infinite set has no end of its elements. E.g D={5,10,15,20\u2026\u2026\u2026\u2026\u2026.}\n<\/li>\n<li>Subset: B is a subset of A if all elements of B are contained in Ai.e it is a smaller set contained in a larger or bigger set. E.g if A = {1,2,3,4,5,6} and B= {2,3,6} then B is a subset of A i.e B \u2282 A\n<\/li>\n<li>Empty set \u0424 or {  }. An empty set or null set contains no element\n<\/li>\n<li>Disjoint set: if two sets have no elements in common, then they are said to be disjoint e.g If P= {2,5,7} and Q= {3,6,8} then P and Q are disjoint.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>OPERATIONS OF SET<br \/>\n<\/strong><\/p>\n<ol>\n<li>Intersection \u2229: the intersection of two sets A and B is the set containing the elements common to A and B e.g if A= {a,b,c,d,e} and B= {b,c,e,f}, then A \u2229 B= {b,c,e}\n<\/li>\n<li>Union \u01b2: the union of A and B, A \u01b2 B is a set which includes all elements of A and B e.g if A = {1,3} and B = {1,2,3,4,6}, then A \u01b2 B ={1,2,3,4,6}\n<\/li>\n<li>Complement of a set: the complement of a set P, P<sup>|<\/sup> are elements of the universal set that that are not in P e.g if U = {1,2,3,4,5,6} P= {2,4,5,6}, then P<sup>|<\/sup>= {1,3}\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Examples<br \/>\n<\/strong>Given that U = {a,b,c ,d,e,f}, P={b,d,e}  Q= {b,c,e,f}<br \/>\nList the elements of<\/p>\n<ol>\n<li>P\u2229 Q      (b)  P \u01b2 Q      (c)  (P \u2229 Q)<sup>|<\/sup>\n\t\t<\/li>\n<\/ol>\n<p>(d)(P \u01b2 Q)<sup>| <\/sup>  (e) P<sup>|<\/sup>\u01b2 Q     (f)Q<sup>|<\/sup>\u2229 P<sup>|<\/sup><\/p>\n<p>\u00a0<strong>Solution<br \/>\n<\/strong><\/p>\n<ol>\n<li>P\u2229 Q = {b,e}\n<\/li>\n<li>P \u01b2 Q= {b, c, d, e, f}\n<\/li>\n<li>\n<div>Since (P \u2229 Q ) = {b, e}\n<\/div>\n<p>Then (P \u2229 Q)<sup>|<\/sup> = {a, c, d, f}\n<\/li>\n<li>Sine (P \u01b2 Q)= {b, c, d, e, f}, then (P \u01b2 Q)<sup>|<\/sup> ={a}\n<\/li>\n<li>\n<div>P<sup>|<\/sup>\u01b2 Q\n<\/div>\n<p>P<sup>| <\/sup>={a, c, f}<br \/>\nQ={b, c, e, f}<br \/>\nTherefore P<sup>|<\/sup>\u01b2 Q={a, b,  c,  e, f}\n<\/li>\n<li>\n<div>Q<sup>|<\/sup> ={a, d}\n<\/div>\n<p>P<sup>|<\/sup>={b, d, e}   = P<sup>|<\/sup>\u2229 Q<sup>|<\/sup> = {d}\n<\/li>\n<\/ol>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>Given that U= {1,2,3,4,5,6,7,8,9,10}, A= {2,4,6,8} B= {1,2,5,9} and C= {2,3,9,10}<br \/>\nFind: a) A\u2229B\u2229C        (b)   C<sup>|<\/sup>\u2229(A\u2229B)        (c) C\u2229(A\u2229B)<sup>| <\/sup>        (d) C<sup>|<\/sup>\u01b2(A\u2229B)<\/p>\n<p>\u00a0<strong>GENERAL EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Given that U= {1,2,3\u2026\u2026\u2026\u202619,20} and A ={1,2,4,9,19,20} B= {perfect square} C={factors of 24}. Where A,B, and C are subsets of universal set U\n<\/div>\n<ol>\n<li>List all the elements of all the given sets\n<\/li>\n<li>Find (i) n(A \u01b2 B)| (ii) n(A \u01b2B \u01b2 C) (iii) n(A<sup>|<\/sup>\u01b2 B<sup>|<\/sup>\u2229 C)\n<\/li>\n<li>Find (i) A\u2229B\u2229C  (ii) A\u01b2(B \u2229 C) (iii) (A<sup>|<\/sup>\u2229 B<sup>|<\/sup>)\u01b2 C\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>List all the subsets of the following sets\n<\/div>\n<ol>\n<li>A={Knife, Fork}\n<\/li>\n<li>P={a, e, i}\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>NGM SSS1 page 71-72, exercise 5b and 5c.<strong><br \/>\n\t\t<\/strong><br \/>\n\u00a0<strong>WEEKEND ASSIGNMENT<br \/>\n<\/strong><\/p>\n<ol>\n<li>If A={a, b, c} B={a, b, c, e} and C={a, b, c, d, e, f} find A\u2229B(A\u01b2C) A.{a,b,c,d}   B. {a,b,c,d,e}    C.{a,b,d,d,e}   D.{a,b,c}\n<\/li>\n<li>If Q={0&lt;x&lt;30,x is a perfect square}, P={x\u00f71\u2264x\u226410,x is an odd number} find Q\u2229P A.{1,3,9} B.{1,9,4} C.{1,9} D.{19,16,25}\n<\/li>\n<\/ol>\n<p>Use the following information to answer questions 3 \u2013 5<br \/>\nA,B and C are subsets of universal set U such that U={0,1,2,3\u2026\u2026..11,12}, A={x:0&lt;x&lt;7}, B={4,6,8,10}, C={1&lt;x&lt;8}<\/p>\n<ol>\n<li>Find (A\u01b2C)<sup>| <\/sup>A{0,1,9} B.{2,3,4,5} C.{2,3,5,7} D.{0,1,2,9}\n<\/li>\n<li>Find A|\u2229 B \u2229C\n<\/li>\n<li>A \u01b2 B<sup>|<\/sup>\u2229 C A.{1,2,3,4,5,6,7} B.{2,3,5,7} C.{6,8,10,12} D.{4,5,7,9,11}\n<\/li>\n<\/ol>\n<p>\u00a0<strong>THEORY<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>The universal set U is the set of integers: A,B and C are subsets of U defined as follows\n<\/div>\n<p>A= {\u2026.., -6,-4,-2,0,2,4,6\u2026\u2026.}<br \/>\nB= {X: 0 &lt;x &lt; 9}<br \/>\nC= {X: -4 &lt; x &lt; 0}<\/p>\n<ol>\n<li>Write down the set A<sup>I<\/sup>, where A<sup>I<\/sup> is the complement of A with respect to U\n<\/li>\n<li>Find B\u2229C\n<\/li>\n<li>Find the members of set B\u01b2C, A\u2229B, and hence show that A\u2229(B\u01b2C)=(A\u2229B)\u01b2(A\u2229C)\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>The universal set U is the set of all integers and the subsets P,Q,R of U are given by\n<\/div>\n<p>P={X: X&lt;0}, Q = {\u2026\u2026,-5-,3,-1,1,3,5\u2026\u2026.}, R= {X: -2&lt;X&lt;7}<\/p>\n<ol>\n<li>Find Q\u2229 R\n<\/li>\n<li>Find R<sup>|<\/sup> where R<sup>|<\/sup> is the complement of R with respect to U\n<\/li>\n<li>Find P<sup>| <\/sup>\u2229 R<sup>| <\/sup>\n\t\t\t\t<\/li>\n<li>List the members of (P\u2229Q)\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>WEEK FOUR\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 TOPIC: IDEA OF SETS CONTENT Notation of Set Types and Operation of Set&#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-2209","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\/2209","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=2209"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2209\/revisions"}],"predecessor-version":[{"id":2210,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2209\/revisions\/2210"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}