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Question:

Let A and B be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set A×B, each having at least three elements is

219

256

228

235

Solution:

Given, n(A)=4, n(B)=2
∴n(A×B)=8
Thus the number of subsets of A×B having at least 3 elements = 28 - 8C0 - 8C1 - 8C2 = 256 - 1 - 8 - 28 = 219