Question

If n(A u B)=23, n(A n B)=9,and n(B)=12. find n(A)

Answer 1

`\boxed{n(A) = 20}`

Explanation:

We know

`n(B)= 12`

From
`n(A \cap B)=9` and
`n(A \cup B)=23`, we conclude
`n(A \cup B)=23 = n(A \cap B) + n(A- B) + n(B- A)`

Once
`n(B)= 12`, then
`n(B- A) = 12-9 = \boxed{3}`

Taking

`23 = n(A \cap B) + n(A- B) + n(B- A) = 9+ n(A- B) +3 = \boxed{12+ n(A- B) }`

Therefore,

`n(A- B) =11 \implies n(A) - 9 = 11 \implies \boxed{n(A) = 20}`