If n(B) = 15, n(A B) = 25, and n(A B) = 3, find n(A).
When in doubt, draw a Venn diagram and fill in the numbers.
The easiest one to start is n(A∩B)=3.
Since n(B)=15, so n(B-A)=12.
n(A-B)=25-(12+3)=10.
Can you find n(A)?
Note:
To type the following symbols, type the characters following the symbol, but without the intervening spaces.
∩ & c a p ;
∪ & c u p ;
∈ & i s i n ;
⊂ & s u b ;
∉ & n o t i n ;
n(B) = 15 n(A∪B)=25, n(A∩B) = 3 find n(A)?
I thought A would equal 10
That's what I got too!
To find the value of n(A), we can use the formula for finding the size of the union of two sets: n(A ∪ B) = n(A) + n(B) - n(A ∩ B).
Given that n(B) = 15, n(A ∩ B) = 3, and n(A ∪ B) = 25, we can substitute these values into the formula to find n(A):
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
25 = n(A) + 15 - 3
Rearranging the equation, we have:
n(A) = 25 - 15 + 3
n(A) = 13
Therefore, n(A) = 13.