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2 Answers
- Anonymous1 decade agoFavorite Answer
Let a ∈ A
Then either A ∈ C or a ∉ C.
If A∈ C then a ∈ (A ∩ C) and thus it is an element of B.
If A ∉ C then since a ∈ (B U C), and a ∉ C, it must be in B.
End proof
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Source(s): PhD in mathematics. A semester of grad level set theory - Awms ALv 71 decade ago
Suppose x is in A.
Then x is in A or x is in B, so x is in A U B.
Since (A ⪠B) â (B ⪠C), x is in B U C. That is, either x is in B or x is in C.
Suppose now that x is not in B, so that x must be in C. However, then x is in both A and C, so x is in A â© C.
Since (A â© C) â B, it follows that x is in B, but this contradicts our assumption that x is not in B.
It follows that x is in B.
