{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Quiz2Sol - by adding 2 to each of the first 8 subsets Thus...

This preview shows page 1. Sign up to view the full content.

COT 3100 Quiz #2 – Sets Name : _______________ Date : 2/1/01 1) (4 pts) Let A= {1, 3, 5, 7, 9}, B= {1, {2, 3}, 4, 5}, C= {1, 2, 3, 4, }, and D={{5}, 6}. List the members of each of the following sets explicitly: a) A B = { 1, 3, 5, 7, 9, 4, {2,3} } b) A – B = { 3, 7, 9 } c) B D = { } d) A (C D) = { 1, 3 } 2) (3 pts) Let A = {2, 3, 5, 7, 11}. For any set X, let sum(X) denote the sum of the elements in the set. For how many different subsets Y of A is sum(Y) an odd number? Consider all the subsets of {3, 5, 7, 11}. The subsets X of odd cardinality all have sum(X) = odd number. There are 2 4-1 = 8 of these subsets total, using the formula given in class on 1/30. Now, we can create 8 more subsets X such that sum(X) = odd
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: by adding 2 to each of the first 8 subsets. Thus, the answer is 2x8 = 16. 3) (7 pts) A, B, C and D are sets such that A ⊂ B and C ⊂ D. Prove that (B ∩ C) ⊂ (A ∪ D). We must show that (B ∩ C) ⊂ (A ∪ D). Essentially, we need to show that if x ∈ (B ∩ C) then x ∈ (A ∪ D). To prove this, assume that x ∈ (B ∩ C). Under this assumption, we must show that x ∈ (A ∪ D). Using the defn of intersection, we find that x ∈ B and x ∈ C. Since C ⊂ D, by the defn of subset we have that x ∈ D. But, we know by the defn of union, that x ∈ A ∪ D....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online