Question

If A = {1, 2, 3}, B = {3, 4, 5}, C = {4, 6}, then A x $(B\cup C)$ =

• A. {(1, 3) (1, 4) (1, 5) (1, 6) (2, 3) (2, 4) (2, 5) (2, 6) (3,3) (3, 4) (3,5) (3, 6)}
• B. A x $(B\cap C)$
• C. B x $(A\cap C)$
• D. all the above

Answer 1

The correct option is A {(1, 3) (1, 4) (1, 5) (1, 6) (2, 3) (2, 4) (2, 5) (2, 6) (3,3) (3, 4) (3,5) (3, 6)}

If A = {1 , 2 , 3} , B = {3 , 4 , 5} , C = {4 , 6}

then, to find A X (B U C)

B U C = combination of unique elements of set B and C.

B U C = {3, 4 , 5, 6}

Using associative property of set:

A X (B U C) = (A X B ) U ( A X C)

To find cartesian products:

(i) A X B = {1 , 2 , 3 } X {3 , 4 , 5}

= {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)}

(i) A X C = {1 , 2 , 3 } X {4 , 6}

= {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}

(A X B ) U ( A X C) = {(1 , 3), (1 , 4), (1 , 5), (2 , 3), (2 , 4), (2 , 5), (3 , 3), (3 , 4), (3 , 5)} U {(1 , 4), (1 , 6), (2 , 4), (2 , 6), (3 , 4), (3 , 6)}

Ans = {(1 , 3), (1 , 4), (1 , 5), (1 , 6), (2 , 3), (2 , 4), (2 , 5), (2 , 6), (3 , 3), (3 , 4), (3 , 5), (3 , 6)}