If A={x belongs to N; 3

Question

42. If \( A=\{x \in N: 3<x<12\} \) and \( B=\{x \in N: x \) is even, \( x<15) \), then (a) \( A \cup B=\{4,6,8,10,12,14) \) (b) \( A \cap B=\{4,6,8,10\} \) (c) \( A / B=\{5,7,9,11,13\} \) (d) \( B / A=\{2,8,12,14\} \)

Answer 1

Correct option is (b) A \(\cap \) B = {4, 6, 8, 10}

A = {x \(\in N \) : 3 < x < 12}

∴ A = {4, 5, 6, 7, 8, 9, 10, 11}

and B = {x \(\in N \) : x is even & x < 15}

∴ B = {2, 4, 6, 8, 10, 12, 14}

Then A \(\cup\) B = {2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14}

A \(\cap \) B = {4, 6, 8, 10}

A/B = A - B = \(\phi\)

B/A = B - A = {2, 12, 14}