Show that if A and B are sets with A ⊆ B, then?
Show that if A and B are sets with A ⊆ B, then
A ∪ B = B
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Show that if A and B are sets with A ⊆ B, then
A ∪ B = B
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Verified answer
By definition of set union, every element of A ∪ B is an element of A or an element of B, or both.
If it's an element of A, then it's also an element of B, because A is a subset of B.
Thus, every element of A ∪ B is an element of B.
By definition of set union, every element of B is an element of A ∪ B.
We have shown that
every element of A ∪ B is an element of B, and
every element of B is an element of A ∪ B.
By definition of set equality,
A ∪ B = B