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Theorem 5(If AsubeB; Show that AxxCsubeB...

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

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

Theorem 5 (distributive Laws)

If A sube B and C be any set , then prove that: A xx C sube B xx 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))

Let A be a non-empty set such that A xx B=A xx C. Show that B=C

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

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