If A and B are finite sets, say with n and m elements respectively, what can you say regarding the sizes of A ∪ B? A ∩ B? A - B?

Question

Mathematics

Deangelo Dalton

1 December, 08:02

If A and B are finite sets, say with n and m elements respectively, what can you say regarding the sizes of A ∪ B? A ∩ B? A - B?

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Answers (1)

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Yin · Answer 1

Answer with explanation:

There are two sets A and B having n and m elements.

N (A) = n

N (B) = m

→N (A ∪ B) = Common as well as non common elements of Set A and Set B.

So, N (A∪B) ≤ m + n

→N (A∩B) = Common elements of Both A and B

N (A∩B)
N (A∩B)
→ N (A∩B) = m or n or m-n or n-m, depending on m>n, or, n> m or if, m=n.

→N (A-B) = Common elements of set A is excluded from set B and remaining elements are written

=n, if there is no common element

= n-m, if there is some common element.