Question

X = {1, 2, 3, 4, 5} what is the number of ordered pairs (Y, Z) where Y and Z are subsets of X and Y intersection Z is an empty set

Answer 1

Answer:

Step-by-step explanation:

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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