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Question

If A = A={xW:5<x<10},B={3,4,5,6,7} and C={x=2n ; n N and n 4 }. Find :

(i) A(BC)

(ii) (BA)(BC)
(iii) B(AC)
(iv) (AB)(AC)

Name the sets which are equal

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Solution

A = B = x = 2n When n = 1, x = 2×1 = 2 When n = 2, x = 2×2 = 4 When n = 3, x = 2×3 = 6 When n = 4, x = 2×4 = 8 C = {2,4,6,8} (i)BC={3,4,5,6,7}{2,4,6,8}={3,4,5,6,7}A(BC)={6,7,8}Ans. (ii)BA={3,4,5,6,7}{6,7,8,9}{3,4,5,6,7,8,9}(BA)(BC)={3,4,5,6,7,8,9}{2,3,4,5,6,7,8}={3,4,5,6,7,8}Ans. (iii)(AC)={6,7,8,9}{2,4,6,8}={6,8}B(AC)={3,4,5,6,7}{6,8}={3,4,5,6,7,8}Ans. (iv) (AB)={6,7,8,9} {3,4,5,6,7}={6,7}(AB)(AC)={6,7}{6,8}={6,7,8} Ans.


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