In a two-column proof, the reasoning of the first step is usually "given." O True O False

Question 7 1 pts Give the missing truth value in the following truth table. Determine if the argument expressed is valid. Note that the conclusion of the argument is located in the rightmost column. PvQ -P PoQ T T F T T T T F T O True, Valid False, Valid O True, Invalid False, Invalid

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Please answer the second question.   Question For these statements:               • State the base case and prove that it is true.               • State the inductive hypothesis               • Outline how would you proceed with the rest of the proof by setting up the inductive proofs. Explain roughly what will exactly happen to complete the proof. It's not actually required to do the complete proof. Just give a conclusion.

Question 12 Complete the TRUTH TABLE by filling in the TRUTH VALUE of the column (m A-p)→r mpr(m1-p)→r FFTT TTFT TFFF FTFT FFFT Blank 1 T.

The following arguments have false conclusions. What is the problem with each argument? A. If a person owns a cat, then they don't own a dog. Dr. Morales owns a cat. :. Dr. Morales doesn't own a dog B. If a number n is even, then 2n is even. The number 2n is even, for n=3 (note: 2n = 6). : The number n is even, for n=3.

For each proof, you must include (i.e., write) the premises in that proof. Proofs must have premises. Conditional Proof (CP), Indirect Proof (IP) and Assumed Premises (AP) are not allowed to be used. Only the 18 rules of inference can be used. Points will be lost if you use any of the inference rules Resolution, Contradiction, Transposition, Idempotence and Identity. Only answer questions 7, 9 and 11.

What relevant conclusion can be drawn from the following promesise. "If I play hockey, then I am sore the next day." "I use the whirlpool if I am sore." "I did not use the whirlpool." O I played hockey. O I'm sore O l use the whirlpool. O I didn't play hockey.