Please do answer it all :))
A.
Direction: prove the following mathematicaltheorem using proof by contradiction.
1. “If n2 is an odd integer, then n is odd.”
2. Prove that p √3 is irrational.
B.
Direction: prove the following mathematicaltheorem using proof by cases.
1. “If n is an integer, then n2 + 3n + 2 is eveninteger”
2. For all integers. If m and n are of the same parity,then m + n is even.
3. “If (n + 1)3 ≥ 3n if n is a positiveinteger with n ≤ 4.
C.
Direction: Let x and y be an integer. Justifyyour answers to each of the following questions by using somedefinitions in basic number theory.
1. Is 8x + 6y even numbers?
2. is 2x2 + 6y + 3 is odd?
3. If x and y are positive, is x2 + 2xy +y2 prime?
4. Is -6 factor of 48?
5. IS x2-1 is odd numbers?
6. If y is odd, then y + y + y is odd?
7. Is 36 multiples of 4?
8. Is the square root of 4 is a positive integer and primenumber?
9. Is 9/5 is a rational number?
10. Is 24 mod 5 is 4?
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