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show that if A is a subset of C and B is a subset of D, then A X B is a subset of C X D. I am confused as to what the question really is, and does it have something to do with the Cartesian product?

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show that if A is a subset of C and B is a subset of D, then A X B is a subset of C X D. I am confused as to what the question really is, and does it have something to do with the Cartesian product?
Answered Same Day Dec 29, 2021

Solution

David answered on Dec 29 2021
120 Votes
Show that if A is a subset of C and B is a subset of D, then A × B is a
subset of C ×D.
Proof:
Let
(x, y) ∈ A×B
we have
x ∈ Aandy ∈ B
But as A ⊂ C, we have x ∈ C and same y ∈ D. This gives
x ∈ C and y ∈ D
(x, y) ∈ C ×D
Which implies A×B ⊂ C ×D.
1
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