mth 1000c mathematical proofs

Attached to the questions are the class notes that can most likely assist you in answering these proofs. **n/2 is supposed to be fraction and n^2 is supposed to represent n to the 2nd power.

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

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

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 n^2 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)

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