Theorem 5(If `AsubeB`; Show that `AxxCsubeBxxC` for any set C

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

If AsubeB , prove that AxxCsubeBxxC for any set C.

If AsubeB , show that AxxAsube(AxxB)nn(BxxA)dot

If AsubeB and BsubeC then show that AsubeC .

Using properties of sets, show that for any two sets A a n d B ,(AuuB)nn(AuuB^(prime))=Adot

Applying the properties of sets prove the identity for any three sets A, B and C. A-(B nn C)=(A-B) uu (A-C)

Theorem 10(Let A and B be non empty set such that A xx B=A xx C. Show that B=C

Theorem 7 (For any set A;B;C;D prove that (A xx B)nn(C xx D)=(A nn C)xx(B nn D)

Theorem 1(i) (For any three set A;B;C; prove that A xx(B uu C)=(A xx B)uu(A xx C))

Theorem 2 (For any three set A;B;C ; prove that A xx(B-C)=(A xx B)-(A xx C)