Quiz 1
Thomas Whitt
Name: KEY
Answer the following questions. They are worth 11 points apiece. The quiz is graded out
of 20 points.
1. Use proof by cases to prove that |x + y| |x| + |y|
There are several ways to prove this. Here are the two I suspect are
Quiz 2
Thomas Whitt
Name: KEY
Answer the following questions. They are worth 11 points apiece. The quiz is graded out
of 20 points.
1. Let x be an integer. Prove that x is a multiple of 3 if and only if x2 is a multiple of 3.
Proof. First we will show tha
Quiz 3
Thomas Whitt
Name: KEY
Answer the following questions. They are worth 11 points apiece.
1. Prove that n! > 2n for all integers n 4. Proof. We proceed by induction on n.
Base Case: For n = 4, n! = 4! = 24 > 16 = 24 = 2n . The result holds for n = 4