155k views
3 votes
Let A and B be sets with cardinal numbers , n(A) = a and n(B) = b respectively . Decide whether the statement is true or false. 2) n(A cup B)=n(A)+n(B)-n(A cap B)

User HelloWorld
by
8.8k points

1 Answer

5 votes

Answer:

True

Explanation:


A\cup B=A\cup(A-B)\\\\A\ and\ A-B\ are\ disjoint\ that\ means\ there\ is\ no\ common\ element\ in\ these\ two.\\\\n(A\cup B)=n(B\cup(A-B))\\\\n(A\cup B)=n(B)+n(A-B)\ \ \ \ \ \ \ as\ for\ disjoint\ set\ P,Q\ n(P\cup Q)=n(P)+n(Q)\\\\(n(P-Q)=n(P)-n(P\cap Q))\\\\n(AUB)=n(B)+n(A-B)\\\\n(AUB)=n(B)+n(A)-n(A\cap B)\\\\n(AUB)=n(A)+n(B)-n(A\cap B)\\\\Hence\ given\ statement\ is\ true

User Feckmore
by
9.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories