[" 2.a) Prove: "],[" i) "A times(B nn C)=(A times B)nn(A times C)],[" ii) "A times(B uu C)=(A times B)uu(A times C)]

Prove that A nn(B uu C) =(A nn B) uu (A nn C)

If A = [1,2,3], B=[4], C= [5] , then verify that: (i) A xx (B uu C) = (A xx B) uu (A xx C) (ii) A xx (B nn C) = (A xx B) nn (A xx C)

Let A=" "{1," "2," "3} , B" "=" "{3," "4} and C" "=" "{4," "5," "6} . Find (i) A xx(B nnC) (ii) (A xxB) nn(A xxC) (iii) A xx(B uuC) (iv) (A xxB) uu(A xxC)

Prove that (A uu B)xx C=(A xx C)uu(B xx C)

By taking suitable sets A,B,C, verify the following result : (i) A xx(B cap C)= (A xx B) cap (A xx C). (ii) A xx(B cup C)=(Axx B) cup (AxxC). (iii) (AxxB) nn (BxxA) = (AnnB) xx (BnnA). (iv) C-(B-A)= (CnnA) uu (CnnB'). (v) (B-A) nn C=(B nn C)-A=Bnn(C-A). (vi) (B-A)uu C=(BuuC)-(A-C).

If A and B and C are three non-empty sets, then which of the following is/are not true ? (A) n(A xx B) = n(B xx C) hArr n(A) = n(C) (B) A - (B nn C) = (A - B) nn (A - C) (C ) A uu (B nn C) = (A uu B) nn (A uu C) (D) (A nn B) - C = (A-C) nn (B - C)

Let A= {1, 2, 3} , B = {3, 4} and C = {4, 5, 6} . Find(i) A xx(B nnC) (ii) (A xxB) nn(A xxC) (iii) A xx(B uuC) (iv) (A xxB) uu(A xxC)

For any three sets A,B,C prove that: A xx(B'uu C')'=(A xx B)nn(A xx C)A xx(B'nn C')'=(A xx B)uu(A xx C)

If A={1,2,3},B={4},C={5}, then verify that: A xx(B uu C)=(A xx B)uu(A xx C)A xx(B nn C)=(A xx B)nn(A xx C)A xx(B-C)=(A xx B)-(A xx C)

For any three sets A, B, C, prove that : Axx(B nn C)=(A xx B)nn (Axx C) .