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Long Quiz 1. True or False. Determine whether the statement is true or false. Justify your answer. In items 1-9, let P and Q be statements. 1. The conditionals "If P then Q" and "If Q then P" are equivalent. 2. The conditionals "P If Q" and "P only if Q" are equivalent. 3. The conditionals "P provided Q" and "P is necessary for Q" are equivalent 4. If Q is true, then P - Q is true. 5. If P - @ is true, then @ Is true. 6. The converse of the conditional P - "Q is Q - ~p. 7. The contrapositive of the conditional "Q - Pis ~P + Q. 8. The statement "@ - P is equivalent to the statement "P - Q. 9. The statement P - " Is equivalent to the statement "P + Q. 10. Both deductive and inductive reasoning are valid forms of reasoning. 1l. Do the following. Write your answer on a separate sheet of paper. 1. State the hypothesis and conclusion in the following conditionals. a. You will enjoy mathematics if you strive to understand it. b. Whales are mammals. c. If a median of a triangle is also an angle bisector, then the triangle is isosceles. d. Corresponding angles formed by parallel lines cut by a transversal are congruent 2. Give the converse, inverse, and contrapositive of the statements in Item 1. 3. Consider the conditional "If two circles intersect, then they intersect at exactly two points." Give the converse, inverse, and contrapositive of this statement. State the truth value of each statement. Fold a piece of lengthwise in half to produce 1 crease. Now fold the paper lengthwise again in half to produce 2 creases. Repeat the procedure for 4 folds. Form a conjecture about the number of creases. 5. Investigate the number of diagonals that can be drawn in a triangle, quadrilateral, penta- gon, and hexagon. Form a conjecture. 6. Investigate the remainders when a perfect square is divided by 3. Form a conjecture