If A x B ⊆ C x D and A ∩ B ∈ ∅, Prove that A ⊆ C and B ⊆ D.

Asked by Aaryan | 1 year ago |  38

##### Solution :-

Given:

A × B  C x D and A ∩ B ∈ ∅

A × B  C x D denotes A × B is subset of C × D that is every element A × B is in C × D.

And A ∩ B ∈ ∅ denotes A and B does not have any common element between them.

A × B = {(a, b): a ∈ A and b ∈ B}

We can say (a, b)  C × D [Since, A × B  C x D is given]

a ∈ C and b ∈ D

a ∈ A = a ∈ C

C

And

b ∈ B = b ∈ D

D

Hence proved.

Answered by Sakshi | 1 year ago

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