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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 ) ∪ P ( B ) = P ( A ∪ B )`? Justify your answer.

Text Solution

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Let A= {0,1} and B ={1,2}
`therefore A cup B ={ 0,1,2}`
`therefore A cup B = { 0, 1, 2 } `
P(A) = {0), {0}, {1}, {0, 1}}
P(B)= {`phi`, {1}, {2}, {1,2}}
`P( A cup B) ={ phi {0},{1},{2},{0,1},{1,2},{0,2},{0,1,2}}`
`P(A) cup P(B)={phi, {0}, {1}, {0,1}, {2}, {1,2}} `
`therefore P(A) cup P(B) ne P ( A cup B)`
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