1.)Which of the expressions is equivalent to the following statement: The sum of

Q: 1.)Which of the expressions is equivalent to the following statement: The sum of

1(d) If x is even and y is even, then x + y is even Explanation: BOTH should be even for the sum to be even 2(d) February Explanation: As we know it can have 28/29 days 3)b. If x is a real number and x 3 4)a. x is rational. 5) c. n = 0, 0 + 0 = 0; n = 1, 1 + 1 > 1; n = 2, 2 + 2 = 22 Thanks, let me know if there is any concern

ID: 3748641 • Letter: 1

Question

1.)Which of the expressions is equivalent to the following statement:

The sum of two even numbers is even.

2.) Find a counterexample for the statement: every month of the year has 30 or 31 days.

3.) If direct proof is used to prove the following statement: If x is a real number and x 3, then 12 - 7x + x*x 0. What is the hypothesis?

4.) If proof by contrapositive is used to prove the following statement: For every real number x, if x is irrational, then -x is also irrational. What is the hypothesis?

5.) Consider the following statement: For every positive integer n less than 3, n + n n2. Which facts must be checked in a proof by exhaustion of the statement?

a.) If x is even or y is even, then x + y

Explanation / Answer

1(d) If x is even and y is even, then x + y is even

Explanation: BOTH should be even for the sum to be even

2(d) February
Explanation: As we know it can have 28/29 days

3)b. If x is a real number and x 3

4)a. x is rational.

5) c. n = 0, 0 + 0 = 0; n = 1, 1 + 1 > 1; n = 2, 2 + 2 = 22

Thanks, let me know if there is any concern

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1.)Which of the expressions is equivalent to the following statement: The sum of

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Explanation / Answer

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