Show that `A ∪ B = A ∩ B` implies `A = B`

Show that A ∩ B = A ∩ C need not imply B = C .

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

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

Show that A cap B=A cap C need not imply B=C.

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 ) .

If A = (5,6),B = (4,5,6), C = (5,6,7), show that A xx A = (B xx B) cap (C xx C )

Show that suma sin(B-C) =0

Let Aa n dB be two 2xx2 matrices. Consider the statements (i) A B=O, A=O or B=O (ii) A B=I_2 implies A=B^(-1) (iii) (A+B)^2=A^2+2A B+B^2 a. (i) and (ii) are false, (iii) is true b. (ii) and (iii) are false, (i) is true c. (i) is false (ii) and, (iii) are true d. (i) and (iii) are false, (ii) is true

Assume that P ( A ) = P ( B ) . Show that A = B