If-A-B-C-and-D-are-any-four-sets-then-i-A-B-C-D-A-C-B-D-ii-A-B-C-D-A-C-B-D-

Question Number 3130 by Rasheed Soomro last updated on 05/Dec/15

I f A, B, C a n d D a r e a n y f o u r s e t s t h e n

(i) (A - B) \cup (C - D) \overset{?}{=} (A \cup C) - (B \cup D)

(i i) (A - B) \cup (C - D) \overset{?}{=} (A \cup C) - (B \cap D)

Answered by prakash jain last updated on 05/Dec/15

(i i)

(A - B) \cup (C - D) = (A \cup C) - (B \cap D)

A = {1, 2, 3, 4, 5}

B = {1, 2, 3, 4, 5}

C = {6, 7, 8, 9}

D = {6, 7, 8, 9}

A - B = \emptyset

C - D = \emptyset

LHS = (A - B) \cup (C - D) = \emptyset

A \cup C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

B \cap D = \emptyset

RHS = (A \cup C) - (B \cap D) = {1, 2, 3, 4, 5, 6, 7, 8, 9}

LHS \neq RHS

Commented by Rasheed Soomro last updated on 06/Dec/15

T^{HAN} K_{S}!

Answered by prakash jain last updated on 05/Dec/15

(i)

A = {1, 2, 3, 4, 5}

B = {2, 3, 6, 7}

C = {2, 3, 8, 9}

D = {6, 7, 8, 9}

A - B = {1, 4, 5}

C - D = {2, 3}

LHS = (A - B) \cup (C - D) = {1, 2, 3, 4, 5}

(A \cup C) = {1, 2, 3, 4, 5, 8, 9}

(B \cup D) = {2, 3, 6, 7, 8, 9}

RHS = (A \cup C) - (B \cup D) = {1, 4, 5}

LHS \neq RHS

Commented by Rasheed Soomro last updated on 06/Dec/15

T_{HAN} K^{S!}