Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ? X, Z ? X and Y n Z is empty, is (1) 52 (2) 35 (3) 25 (4) 53

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M.MURALIKRISHNA
askIITians faculty

Dear Student,
Please find below the solution to your problem.

Y⊆X,Z⊆X
Let a∈X, then
a∈Y,a∈Z.....(1)
a∈/​Y,a∈Z.....(2)
a∈Y,a∈/​Z.....(3)
a∈/​Y,a∈/​Z.....(4)
We require Y∩Z=φ
Thus, for a, equation (1),(2) and (3) can satisfy Y∩Z=φ
Therefore,
Y∩Z=φ has 3 options.
Thus,
No. of required possibilities for 5 elements of X = 3^5

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