SOLUTIONS TO HOMEWORK 1 AND 2
YU SUN AND LONG CHEN
1. S OLUTIONS TO H OMEWORK 1
Homework: p10: 5, 12; p19: 5, 17; p28: 15.
1.2 5. First note that A B = A B C
1
and thus
CC
C
A (A B ) = A (A B ) = A (A B ) = A B,
1 for a set, S C is the
complement of S
The
Math 104, Solution to Quiz 8
Instructor: Guoliang Wu July 21, 2009
1. (15 points) Prove that the following equation has at least one real solution in (0,1): 3 2 ex = x + . 2 Proof. Let f (x) = ex (x + 3 ). Then f is continuous on [0, 1]. 2 3 1 = < 0; 2 2
Dept. of Math. Sci., WPI
MA 1034 Analysis 4
Bogdan Doytchinov, Term D03
Homework Assignment 3
Solutions
1. Let A, B IRn . Prove that (intA) (intB) = int(A B). Is the statement true if
intersection is replaced by union? Explain.
Solution. To show that two