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Let Z be the set of integers. If A = {x ...

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 is

A

`2^(12)`

B

`2^(18)`

C

`2^(15)`

D

`2^(10)`

Text Solution

Verified by Experts

The correct Answer is:
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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