Question

If Ax B = {(1,2), (2,3), (1,3), (2,3)} then find n(Ax B). Ans:4​

Answer 1

Answer:

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)}