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Let A(1), A(2),……A(m) be m sets such tha...

Let `A_(1), A_(2),……A_(m)` be m sets such that `O(A_(1))=p, AA i=1,2,….m and B_(1), B_(2)…..B_(n)` be n sets such that `Q(B_(1))=q AA j=1,2,……n`. `"If " underset(i=1)overset(m)UA_(i)=underset(j=1)overset(n)UB_(i)=S` and each of element S belongs to exactly `alpha` number of `A_(i)'s and beta` number of `B_(j)S` then,

A

pm=nq

B

`alphapm=betanq`

C

`betapm=alphanq`

D

`(pm)^(beta)=(nq)^(alpha)`

Text Solution

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The correct Answer is:
C
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