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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
(Continued )
To prove this inclusion, we need to show that if t A × (B C), then t (A × B) (A × C). Because t is the
element of the Cartesian product of two sets, namely A and (B C), t has two coordinates. So, we can write
t =(x, y)withx A and y (B C). Thus, t =(x, y)withx A and either y B or y C. Therefore, t =(x, y)
with either x A and y B or x A and y C. This implies that t =(x, y) with either (x, y) A × B or
(x, y) A × C.
So, we can conclude that (x, y) (A × B) (A × C). So t (A × B) (A × C).
Second part: A × (B C) (A × B) (A × C)
To prove this inclusion, we need to show that if t (A × B) (A ×
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Publisher Resources

ISBN: 9780123822178