I came up with this question
If A is a subset of B , then A intersection B = A
If $A \subseteq B$ , then $A \cap B = A$
Can anyone please explain me how to do it? Thank you so much!
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Graham Kemp
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lasan manujitha
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1Elements of intersection are elements of $A$ and $B$. But we can leave out the part "and $B$", because elements of $A$ are automatically elements of $B$ since $A$ is a subset of $B$. – drhab May 18 '19 at 10:38
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As an aside, I think you.ahould review the difference between "I came up with this question" and things like "I came upon this question". – Mark S. May 18 '19 at 12:50
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If A is a subset of B, then all elements of A are found in B. So their common elements, their intersection, is exactly the A set. An example: A={x; y} B={x; y; z} A ⊆ B, because x ∈ A, x ∈ B and y ∈ A, y ∈ B (! z ∈ B, but z ∉ A, so A≠B) A∩B={x; y}∩{x; y; z}={x; y}=A
Sofia Smith
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You don't normally have to do a demonstration, because the final statement is obvious, but you can use it, if you need one. – Sofia Smith May 18 '19 at 12:47
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