Question

Assume that $P\left(A\right)=P\left(B\right)$. Show that $A=B$Is it true that for any sets $A$ and $B,P\left(A\right)\cup P\left(B\right)=P(A\cup B)$? Justify.

Answer 1

Given,P(A)=P(B)

A=B ,let A={1,2,3} so B is also equals to={1,2,3}

P(AUB)={1,2,3}

P(A)UP(B)={1,2,3}

So P(A)∪P(B)=P(A∪B) is true for any set if A=B