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MATH 31011 - Homework II Solutions for Section 010 by Joel S. Beil (Summer I 2005), Assignments of Discrete Mathematics

Kent State University (KSU) - Ashtabula CampusDiscrete Mathematics

Solutions for problems 1-4 of the homework assignment for math 31011 - section 010, taught by joel s. Beil during the summer i 2005 semester. The problems involve set theory and functions, including the relationship between the images of intersections and the intersections of images under a function.

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Pre 2010

Uploaded on 08/01/2009

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MATH 31011 Summer I 2005
Section 010 Joel S. Beil
Name:
HOMEWORK II
For problems 1-4, let f:A→B,S,T⊆Aand U,V⊆B.
(1) Show that f(S∩T)⊆f(S)∩f(T).
(2) Is it true that f(S)∩f(T)⊆f(S∩T)? If so, prove it.
(3) Prove that f−1(U∩V) = f−1(U)∩f−1(V).
(4) Suppose that S⊆Aand that Ais countable (finite or infinite). Show that Sis also countable.
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MATH 31011 Summer I 2005 Section 010 Joel S. Beil

Name:

HOMEWORK II

For problems 1-4, let f : A → B, S, T ⊆ A and U , V ⊆ B. (1) Show that f (S ∩ T ) ⊆ f (S) ∩ f (T ). (2) Is it true that f (S) ∩ f (T ) ⊆ f (S ∩ T )? If so, prove it. (3) Prove that f −^1 (U ∩ V ) = f −^1 (U ) ∩ f −^1 (V ). (4) Suppose that S ⊆ A and that A is countable (finite or infinite). Show that S is also countable.