Mathematics, 19.05.2020 22:08 bqg464
Consider the following theorem. Theorem: For all sets A and B, if A β B, then A βͺ B β B. Supply explanations for the steps in the proof of the theorem. Proof: Statement
Explanation Suppose A, B, and C are any sets such that A β B. starting point We must show that A βͺ B β B. conclusion to be shown Let x be any element in A βͺ B.
start of an element proof Then x is in A or x is in B.
In case x is in A, then x is in B
In case x is in B, then x is in B.
tautology (p β p) So in either case, x is in B. proof by division into cases Thus every element in A βͺ B is in B.
since x could be any element of A βͺ B Therefore, A βͺ B β B [as was to be shown]."
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Consider the following theorem. Theorem: For all sets A and B, if A β B, then A βͺ B β B. Supply expl...
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