Handwritten 2. Submission must be in pdf format 3. Filename: Surname_SA2.1.PDF 4. For full points: show a complete solution Activity 1. (40 pts.) Proving using Mathematical Induction a. Let P(n) be the statement that 1 2
+2 2
+⋯+n 2
=n(n+1)(2n+1)/6 for the positive integer n. b. 2n4 2. (50pts) Determine whether the following argument is valid: (Show your solution) (a) . Given the premises: (1) p→q; (2) q→(r∧s);(3)¬r∨(−ℓ∨u);(1)p∧t. Conclusion: u. (b) If Superman were able or willing to prevent evil, he would do so. If Superman were unable to prevent evil, he would be impotent; if he were unwilling to prevent evil, he would be malevolent. Superman does not prevent evil. If Superman exists, he is not impotent or not malevolent. Therefore, Superman does not exist. 3. P7 (10 pts.)Proving Prove that if m and n are integers and mn, is even, then m is even or n is even.|