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