Fsc Part 1 Mathematics (Complete Solution)

Q3
Under what conditions on A and B are the following statements true?

(i) AUB=A

SOLUTION:

If B⊆A,then AUB=A

(ii) AUB=B

SOLUTION:

If A⊆B ,then AUB=B

(iii) A-B=A

SOLUTION:

If A=Φ, then A-B=A

(iv) A∩B=B

SOLUTION:

If B⊆A, then A∩B=B

(v) n(AUB)=n(A)+n(B)

SOLUTION:

If A∩B=Φ , then n(AUB)=n(A)+n(B)

(vi) n(A∩B)=n(A)

SOLUTION:

If A⊆B,then n(A∩B)=n(A)

(vii) A-B=A

SOLUTION:

If A∩B =Φ,then A-B=A

(viii) n(A∩B)=0

SOLUTION:

If A∩B=Φ ,then  n(A∩B)=0

(ix) AUB=U

SOLUTION:

If B=A' ,then  AUB=A

(x) AUB=BUA

SOLUTION:

For any two sets A and B, AUB=BUA it holds always.

(xi) n(A∩B)=n(B)

SOLUTION:

If B⊆A, then n(A∩B)=n(B)

(xii) U-A=Φ

SOLUTION:If A=U , then U-A=Φ

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