# Hello, so the switch from face to face classes to online is really

tough and my professor is literally throwing math exercises at us and I have no idea what to do. We are doing Proofs and Computations. It's really hard to search online and find websites that will help me understand how to solve it because he doesn't really have a title for what type of math we are doing. The course in Math 1000c.

Exercises

Prove: There are infinitely many composites that end in 7. (Not a contra- diction proof.)

Prove: If n is an odd integer, then n is not an integer. 2

Prove: If r and s are numbers, r is an integer and s is not an integer, then r + s is not an integer.

Prove: If n is an integer and n2 is an odd integer, then n is an odd integer.

Prove: If n is an integer, p is a prime and p divides n, then p does not divide n+1.

Prove: If there are 500 people in a room, then at least two of them have the same birthday (month and day)

Computations. Find the gcd and lcm of each of the following. Compute the product of the two numbers. Compute the product of the gcd and lcm and compare your answers.

1. 36 and 48

2. 77 and 49

3. 66 and 132

4. 40 and 75

5. 28 and 44

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