Prove that if n is an integer and 3n+2 is even, then n is even using a proof by contradiction. Rank the options below. As 3n is even and n is odd, 3n- n should be odd, but 3n-n= 2n is even. This is a contradiction. Since 3n+2 is even, so is 3n. Suppose that 3n+2 is even and that n is odd. We know that if we subtract an odd number from an even number, we get an odd number. Therefore, our supposition was wrong; hence n is even.

Consider the following statement. There is an integer n such that 2n² - 5n + 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n² - 5n+ 2) satisfies the property "2n² - 5n + 2 is prime." Show that you can do this by entering appropriate values for n and 2n² - 5n + 2. (n, 2n² - 5n + 2) = 3 X

3. Even great mathematicians make mistakes. Euler used the formula ₁ = 1+x+x²+x³+….. 1 1+x and 1 + 2 + 4 + 8 +... = −1 (by substituting in 2 to deduce that 1 - 1+1 − 1 + ... x = -1 and x = 2 respectively). What was his error? =

Which of the following is the contrapositive of the sentence " If n²+4n+5 is odd, then n is even"?