Question

Prove that using: X ∩ (Y ∪ Z ) =(X∩Y) ∪ (Y ∩ Z )

Listing Method; or
Membership Table.

Given
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {2, 5, 8, 9}
Y = {1, 4, 6, 7, 8}
Z = {5, 7, 9}

Answer 1

There should be a typo in the question: the correct formula would be

`X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)`

Let's compute
`X\cap (Y\cup Z)` first. We have

`(Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}`

If we intersect this set with X, we have

`X\cap (Y\cup Z) = \{5, 8, 9\}`

So, that would be the left hand side. For the right hand side, we have

`X\cap Y = \{8\},\quad X\cap Z = \{5,9\}`

And their union is again
`\{5,8,9\}`