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Let Z be the set of integers. If `A= { x in Z : 2^((x+2)(x^(2)-5x+6)) =1}` and `B={x in Z: -3 lt 2x -1 lt 9},` then the number of subsets of the set ` A xx B`, isA. `2^(12)`B. `2^(18)`C. `2^(15)`D. `2^(10)` |
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Answer» Correct Answer - C Given, set `A={x in Z: 2^((x+2)(x^(2)-5x+6))=1}` Consider, `2^((x+2)(x^(2)-5x+6))=1=2^(@)` `rArr (x+2)(x-3)(x-2)=0` `rArrx=-2, 2, 3` `rArr A={-2,2,3}` Also, we have set `B={x in Z: -3 lt 2x-1 lt 9}` Consider, `-3 lt 2x -1 lt 9,x in Z` `rArr -2 lt 2x lt 10, x in Z` `rArr -1 lt x lt 5, x in Z` `rArr B={0,1,2,3,4}` So, `A xx B` has 15 elements. ` therefore " Number of subsets of "A xx B=2^(15)`. [ `because ` If n(A) = m, the number of possible subsets = `2^(m)`] |
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