Question

If A = {1, 2, 3}, B = {3,4}, C ={ 4, 5, 6}. Find A X (BUC)
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Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

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)}