" Q.11"quad " If "A sube B," prove that "A times C sube B times C" for any set "C" ."

If A sube B, prove that A xx C sube B xx C for any set C.

(i) If A sube B , prove that A xx A sube (A xx B) nn (B xx A) (ii) If A sube B , prove that A xx C sube B xx C for any set C.

Theorem 5 (If A sube B; Show that A xx C sube B xx C for any set C

If A sube B , prove that AxxC sube BxxC for any set C.

If A-B=O/ Prove that A sube B

If A sube B , prove that AxxA sube (A xxB) nn (BxxA) .

If A sube B and C sube D , then prove that: A xx C sube B xx D

If A sube B and C sube D , then prove that: A xx C sube B xx D

If A sube B and C sube D, prove that A xxbar(C)sube B xx D

Prove that A sube B,B sube C rArr A sube C