Question

# 35. Let A={xe W, the set of whole numbers and 3 < 3}, B = {xe N, the set of natural numbers and 25x<4} and C={3,4}, then how many elements will (AUB) x C contain? 2012 II (a) 6 (b) 8 (c) 10 (d) 12.

Solution

$A=\left\{0,1,2\right\}\phantom{\rule{0ex}{0ex}}B=\{2,3\}C=\{3,4\}\phantom{\rule{0ex}{0ex}}A\cup B=\left\{0,1,2,3\right\}\phantom{\rule{0ex}{0ex}}n(A\cup B)=4\phantom{\rule{0ex}{0ex}}n\left(c\right)=2\phantom{\rule{0ex}{0ex}}n(A\cup B\times C)=4\times 2\phantom{\rule{0ex}{0ex}}=8\phantom{\rule{0ex}{0ex}}\mathit{A}\mathit{n}\mathit{s}\mathbf{.}\mathbf{}\mathit{b}\mathbf{)}\mathbf{}\mathbf{8}.$