Question 9315 – GATE 2006

Let X, Y, Z be sets of sizes x, y and z respectively. Let W = X×Y and E be the set of all subsets of W. The number of functions from Z to E is:

Correct Answer: D

Question 2 Explanation:

A set consists of n elements then no. of possible subsets are 2ⁿ.
A set ‘P’ consists of m elements and ‘Q’ consists of n elements then total number of function from P to Q is mⁿ.
⇒ E be the no. of subsets of W = 2^|w| = 2^|xxy| = 2^xy
No. of function from Z to E is = (2xy)^z = (2xy)^z = 2^xyz

Z²^xy

Z×2^xy

Z²^x+y

2^xyz

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