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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
Let x
f F
A
f
. B y definiti on of complement, this implies that x
f F
A
f
. By definition of
union, the fact that an element does not belong to the union implies that the element fails to belong
to e very one of the sets us ed in t he union. So, x
f F
A
f
implies that x A
f
for all f F.
By definition of complement of a set, this is equivalent to stating that x A
f
for all f F.So
x ∈⋂
f F
A
f
. Therefore
f F
A
f
⊆⋂
f F
A
f
.
Second part:
f F
A
f
⊇⋂
f F
A
f
.
Let x ∈⋂
f F
A
f
. By definition of intersection, the element x will be in the intersection o nly if it
belongs to every set in the int ersection. By definitio n of complement, this imp ...
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Publisher Resources

ISBN: 9780123822178