Q. 6 B5.0( 3 Votes )

Prove that:
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Answer :

To prove: (A B) × C = (A × C) (B×C)


Proof:


Let (x, y) be an arbitrary element of (A B) × C.


(x, y) (A B) × C


Since, (x, y) are elements of Cartesian product of (A B)× C


x (A B) and y C


(x A and x B) and y C


(x A and y C) and (x Band y C)


(x, y) A × C and (x, y) B × C


(x, y) (A × C) (B × C) …1


Let (x, y) be an arbitrary element of (A × C) (B × C).


(x, y) (A × C) (B × C)


(x, y) (A × C) and (x, y) (B × C)


(x A and y C) and (x ϵ Band y C)


(x A and x B) and y C


x (A B) and y C


(x, y) (A B) × C …2


From 1 and 2, we get: (A B) × C = (A × C) (B × C)


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