Please explain this question

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∩Z is empty, is

let an element aX
therefore following are the cases:
1. aY and aZ2. aY and aZ3. aY and aZ4. aY and aZ1.aY and aZ2.aY and aZ3.aY and aZ4.aY and aZ
since the given condition is YZ=ϕ
therefore for any element of X , there are 3 ways.
either it is an element of Y or it is an element of Z or it is neither the element of Y nor Z
thus the number of ordered pairs = 3*3*3*3*3 = 35

hope this helps you

  • 1
What are you looking for?