Set cardinality??

Question

n(A)={1,2,3,4,8}
n(B)={5,6,7,2,3}
n(C)={2,6,9,10}
U={1,2,3,4,5,6,7,8,9,10}
Question:

n(AuB)=?
n(AuC)=?
n(AuBuC)=?
n(BuC)=?

*n means cardinality
( ) means of
(A) the set name

Please answer this question

Answer 1

These are easy enough to do by counting elements but if you want a more general approach you may use
n(AUB)=n(A)+n(B)-n(A ^B) where ^ stands for intersection.
n(AUB)=5+5-2=8
n(AUC)=5+4-1=8
n(BUC)=5+4-2=7
n(AUBUC)=n(A)+n(B)+n(C)-n(A^B)-n(A^C)-n(B^C)+n(A^B^C)
n(AUBUC)=5+5+4-2-1-2+1=10

Answer 2

The cardinality is basically the size of a set. The cardinality of A is 5 because there are 5 elements.

n(AuB) is the set containing elements found in both A and B, which is only 2 and 3, so the cardinality is 2.

n(AuC) = 1, only 2 is in both.
n(AuBuC) = 1, only 2 is in all 3
n(BuC) = 2, they share 2 and 6

Answer 3

AUB={1,2,3,4,8, 5,6,7}
n(AuB)=8

AUC={1,2,3,4,8,6,9,10}
n(AuC)=8

AUBUC={1,2,3,4,8,5,6,7,9,10}
n(AuBuC)=10

BUC={5,6,7,2,3,9,10}
n(BuC)=7

Answer 4

this exact question ahs been asked a few minutes ago

exactly

where is this from????