# T Type Proof Used Case Prove Theorem C Last Line P P First Line C B C D Inference C Constr Q24067960

Please solve the all the questions below. Thanks.Especially pay attention to 2nd question.

t, which type of proof is being used in each case to prove the theorem (A → C)? Last Line 겨 (p A -p) 겨 First Line a C b. C d. (some inference) C Construct a contrapositive proof of the following theorem. Indicate your assumptions and conclusion clearly 2. If you select three balls at random from a bag containing red balls and white balls, then at least two of the selected balls will have the same color 3. Write a direct proof of the following theorem. For all odd integers, n, (nA3 + 3) is even. Let P(x) be the proposition: Given positive integer x, for all positive real numbers a and b, (a + b)1x >= a^x + b^x 4. Prove P(0) using a vacuous proof. 5. Write a proof by contradiction of this theorem: Given positive integers x and y, if (x * y) = 1 then (x = y) Show transcribed image text

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