By T. G. Kulkarni, M. K. Kelkar

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Similarly A U F = B l J f = - A o r B . e. = ) l \ . Finally, c n f = £>riF' EX. 3. A = \ 0, 1, 2, 3 subsets has the set A ? ) 0. 3 (, oiB. Since C = D, = and ('•' C = D) ; Write down all the subsets of A. 1 C f| £ = O f| ® this s h ° w s that (i ) , the empty set, is a subset of every set A ; (ii) Subsets of A with one element only are ) 0 (, ) 1 | , ) 2 ^, ) 3 { ; (iii) Subsets of A with two elements only are J I, 2 j 1, 3 and \ a, 3 ( ; ) 0, 1 j 0, 2 j ; ( i v ) Subsets of A with three elements are ) 0 1 , 2 ^ , j 0, 1 , 3 j , \ 0, 2, 3 [ and j 1, 2.

E. 74 elements. B u t we are H e n c e the sets A and B are not disjoint. 62 i- e , 12 elements in common Hence Plain area B ; Shaded area B ' . Fig 23 To show that ( A u # > Proof : n B' = A only if A D B = 0 . W e have the property that intersection of sets is distributive over the union of sets. '. (A UB )f1 B = ( A 0 B') u ( B O B' ) = UnB')u<*>. ) = iflB'. If A n B = (j>, then A and B are disjoint sets and intersect and A C S and hence A f ) B' = A- hence A and B do not Chapter 2 Real Numbers ( l ) Natural numbers.

E. = { 6 , 1 2 , 18, Or j 4 f l C = ^ * | * i s a multiple of 6, * > 0 {. It may b e noted that both A U C and A (~) C are infinite sets. ( i v ) A U £ = ! 2 , 4 , 6, ; and 3, 9, 15, . . 45 | i. e. A (J E is the set of all even integers ( > 0 ) and odd multiplies of 3 between 1 and 50. Similarly it is evident that = ) 6 12, 18, 24, A f \ E = $ * | * i s a multiple of 6 ; 1 < * < 50 (. 48 ( ; or { v ) W e leave it to the students to show that E U F = ) 3, 6, 0 48 ; 5, 10, 20, 25, 35, 40, 50 $ = ) * | * is a multiple of 3 and x > 0 ; * is a multiple of 5 and 1 < * < 50 B f ) F = ] 15- 30, 45 j.

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College Algebra For First Year And Pre-Degree Students by T. G. Kulkarni, M. K. Kelkar


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