I would like the answers to these questions so I can compare them to what i got. Problems1. Show that p = ¬p → (r ^ ¬r) with a truth table. Why does this illustrate the validity of a proofby contradiction?2. Use a direct proof to show that the sum of two odd integers is even.3. Prove that the product of two rational numbers is rational.4. Prove the following theorem:"If A and B are sets, then P(A n B) C P(A) N P(B)."5. Show' that for an integer n, n is odd if and only if 3n + 2 is odd. (Hint: consider proving onedirection by contraposition.)6. Show that Va E R*, Vn E N, if a" ¢ Q then a ¢ Q.7. Use a proof by contradiction to show that v3 is irrational?.8. Prove that n² +n is even for any integer n. (Hint: consider a proof by cases.)9. Prove that 3!z € Z(Vx € Z(xz = x)).10. Determine if the following proposition is true or false. If it is true, provide a proof. If it is false,state the negation of the proposition and provide a proof of the negation."3x, y E Q such that x ¢ Q."

Name: I would like the answers to these questions so I can compare them to w
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: I would like the answers to these questions so I can compare them to what i got. Problems1. Show that p = ¬p → (r ^ ¬r) with a truth table. Why does this illustrate the validity of a proofby contradiction?2. Use a direct proof to show that the sum of