Question

Giren A = {1, 2, 3} , B= { 2, 3,5} ,= {3, 4} and D = {1,3,5}
check if (AnC) x (BnC) = (A (Ax B) n(CXD) is true ?​

Answer 1

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True

Explanation:

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

A ∩ C = {1,2,3} ∩ {3,4} 

= {3} 

B ∩ D = {2,3, 5} ∩ {1,3,5} 

= {3,5} 

(A ∩ C) x (B ∩ D) = {3} x {3,5} 

= {(3, 3)(3, 5)} … (1) 

A x B = {1,2,3} × {2,3,5} 

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

C x D = {3,4} × {1,3,5} 

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

(A x B) ∩ (C x D) = {(3, 3) (3, 5)} … (2)

From (1) and (2) we get 

(A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D) 

This is true.

Hope it will helps you...

Answer 2

True

Explanation:

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

A ∩ C = {1,2,3} ∩ {3,4} = {3}

B ∩ D = {2,3, 5} ∩ {1,3,5} = {3,5}

(A ∩ C) × (B ∩ D) = {3} x {3,5} = {(3, 3)(3, 5)} … (1)

A × B = {1,2,3} × {2,3,5}

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

C × D = {3,4} × {1,3,5}

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

(A × B) ∩ (C × D) = {(3, 3) (3, 5)} … (2)

From (1) and (2) we get

(A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D)