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

No, it is not true. Take A = 1, 2 ad B = 2, 3 ThenA B = 1,2,3 P(A) = , 1 , 2 , 1,2 P(B) = , 2 , 3 , 2,3 P(A) P(B) = , 1 , 2 , 3 , 1,2 , 2,3 . . (i) A B = 1,2,3 P(A B) = , 1 , 2 , 3 , 1, 2 , 2, 3 , 1, 3 , 1, 2, 3 . . . (ii) From (i) and (ii), we have P(A B) P(A) P(B)

Is it true that for any sets A and B,P(A) P(B) = P(A B)?Justify y…

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Is it true that for any sets A and B,$P(A) \cup P(B) = P(A \cup B)?$Justify your answer.

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No, it is not true.
Take A = {1, 2} ad B = {2, 3}
Then$A \cup B = \{ 1,2,3\} $
$P(A) = \{ \phi ,\{ 1\} ,\{ 2\} ,\{ 1,2\} \}$
$P(B) = \{ \phi ,\{ 2\} ,\{ 3\} ,\{ 2,3\} \}$
$\therefore P(A) \cup P(B) = \{ \phi ,\{ 1\} ,\{ 2\} ,\{ 3\} ,\{ 1,2\} ,\{ 2,3\} \} $. . (i)
$A \cup B = \{ 1,2,3\}$

$P(A \cup B) = \{ \phi \}$,{1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}} . . . (ii)
From (i) and (ii), we have
$P(A \cup B) \ne P(A) \cup P(B)$

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