true or false : (A x B) ∩ (C x D) (A ∩ C) x (B ∩ D) for any 4 sets A,B,C,D where ∩ is intersection?
please help me. I am unable to do it
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please help me. I am unable to do it
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(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)
(x, y) ∈ (A x B) ∩ (C x D) <==>
(x, y) ∈ (A x B) and (x, y) ∈ (C x D) <==>
(x ∈ A and y ∈ B) and (x ∈ C and y ∈ D) <==>
(x ∈ A and x ∈ C) and (y ∈ B and y ∈ D) <==>
x ∈ A ∩ C and y ∈ B ∩ D <==>
(x, y) ∈ (A ∩ C) x (B ∩ D)