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If n elements are common in sets A and B...

If `n` elements are common in sets A and B, then prove that `n^(2)` elements will be common in the set `AxxB and BxxA`.

Text Solution

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The correct Answer is:
N/a
`(AxxB)nn(CxxD)=(AnnC)x(BnnD)` (From Ex. 9)
`:. (AxxB)nn(BxxA)=(AxxB)xx((BnnD)`
Now, no. of elementso in `AnnB=n`
and no. of element in `AnnB=n`
`rArr`. No. of elemetns in `(AnnB)xx(BnnA)=nxxn`
`rArr` No. of elements in `(AxxB)nn(BxxA)=n^(2)`
`:.` No,of common elements in `AxxB and BxxA =n^(2)`
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