A) 256
B) 220
C) 219
D) 211
Correct Answer: C
Solution :
\[A=\{x,\text{ }y\}\] \[B=\{a,\text{ }b,\text{ }c,\text{ }d\}\] \[A\times B\]having\[2\times 4=8\] elements Total subsets of\[A\times B\]is\[{{2}^{8}}=256\] \[\therefore \]Total no. of subsets of\[A\times B\]having 3 or more elements \[=256-\left( \underset{\begin{smallmatrix} null \\ set \end{smallmatrix}}{\mathop{1}}\,+\underset{\begin{smallmatrix} \sin gle\,ton \\ set \end{smallmatrix}}{\mathop{8}}\,+\underset{\begin{smallmatrix} subset\,having \\ 2\,elements \end{smallmatrix}}{\mathop{^{8}{{C}_{2}}}}\, \right)\] \[=256-1-8-28=219\]
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