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16. If A = {a, b}, B={x, y), C={a, c, y) then verify thati) A x (BUC) = (A x B) (A x C)

Answer»

Answer:

GIVEN,

A={a, B}

B={x, y}

C={a, c, y}

Step-by-step explanation:

To verify,

L.H.S.

(B union C) ={x, y} union {a, c, y}

={x, y, a, c}

A x (B union C) ={a, b} x {x, y, c, a}

={(a, x) (a, y) (a, c) (a, a) (b, x) (b, y) (b, c) (b, a)}

R.H.S

A x B={a, b} x {x, y}

={(a, x) (a, y) (b, x) (b, y)}

A x C={a, b} x {a, c, y}

={(a, a) (a, x) (a, c) (a, y) (b, a) (b, c) (b, y)}

(A x B) (A x C) ={(a, x) (a, y) (b, x) (b, y) (a, a) (b, a) (a, c) (b, c)}

THEREFORE A x (BUC) =(A x B) (A X C)

HENCE proved


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