Show that for any sets A and B,
`A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )`

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

For any two events A and B , P (A cap B) is :

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

Show that A ∪ B = A ∩ B implies A = B

Show that if A ⊂ B , then C – B ⊂ C – A .

Using properties of sets, show that A ∪ ( A ∩ B ) = A

Consider the sets A and B of Example 12. Find A ∩ B .

Show that the following four conditions are equivalent : (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A

Show that the following four conditions are equivalent : (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A