Let A and B be two finite sets such that $n(A - B)$, $n(A\cap B)$, $n(B - A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If \(n(A\cup…

Question

Let A and B be two finite sets such that $n(A - B)$, $n(A\cap B)$, $n(B - A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If $n(A\cup B) = 18$, then $n(A) + n(B)$ is ____

Accepted Answer

A - 24. Let the three counts be x-d, x, x+d. The union is 3x = 18, so the intersection is x = 6. n(A)+n(B) = n(union) + n(intersection) = 18 + 6 = 24.

Answer

B - 27

Answer

C - 30

Answer

D - 36

Let A and B be two finite sets such that \(n(A - B)\), \(n(A\cap B)\), \(n(B - A)\) are in an arithmetic progression. Here \(n(X)\) denotes the number of elements in a finite set \(X\). If \(n(A\cup…

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