Assignment 5

Assignment 5 - Assignment #5 Section 2.2 13b) Since A is a...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 2.2 13b) Since A is a subset of A U B, every subset of A is a subset of A U B Thus P(A) is a subset of P(A U B). Similarly, P(B) is a subset of P(A U B). Thus, P(A) U P(B) is a subset of P(A U B) 13c) Let A={2} and B={1}. The P(A) U P(B)={{},{2}}U{{},{1}} while P(A U B)={{},{1},{2},{1,2}}. In general, if A is a subset of B or B is a subset of A, then P(A U B)=P(A) U P(B) 16b) Let B be contained in the Reals. Then 0 is in B*, so B* is not empty. 16c) Suppose B=B*. Then it is clear that 0 is in B. Next, suppose 0 is already in B then B* = B U {0} = B 16d) 0 is in B*, so (B*)* = B* by (c) 16e) (A U B)* = (A U B) U {0} by definition = A U (B U {0}) = A U B* But we can also write (A U B)* = (B U A) U {0} = B U (A U {0}) = B U A* That is, we have A U B* = B U A*. Note that either way 0 is already in the set. Applying part (c), we have (A U B)* = A* U B* 17b) Grade C. Need to state x belongs to A-C first, as well as x belongs to B-C afterwards. 17c) Grade A 17f) This is a false claim. Section 2.3 1) f) union is {1,2,. ..,19}, intersection is empty h) Union is [ -(pi), positive infinity) Intersection is [ -(pi), 0] j) Union is the set of all integers Intersection is {0} k) Union is (0,7/3) Intersection is [1/3,2] l) Union is (negative infinity, positive infinity) Intersection is is { } m) Union is R-Z (the set of all real numbers but not include all the integers.) Intersection is { } n) Union is (-infinity, 1) Intersection is (-1, 0] 2)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/18/2012 for the course MAT 108 taught by Professor Staff during the Winter '10 term at UC Davis.

Page1 / 4

Assignment 5 - Assignment #5 Section 2.2 13b) Since A is a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online