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Is it true that for any sets A and B, P...

Is it true that for any sets A and B, `P (A) uuP (B) = P (Auu B)`? Justify your answer.

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Let A and B two sets such that
`A = {a} and B={b}`
then subset of `A = phi, {a}` and subsets of `B = phi,{b}`
Therefore, `P(A) = {phi,{a}} and P(B) = {phi,{b}}`
then `P(A) cup P(B) = {phi,{a}},{b}}`…(1)
Now, `A cup B = {a,b}`
`:. P(AcupB)={phi,{a},{b},{a,b}}`....(2)
It is clear from equations (1) and (2) that `P(A) cup P(B) ne P(A cup B)`
Therefore, for sets A and B, it is not true that `P(A)cupP(B)=P(A cupB)`.
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