Each of the statements below is an implication. In these statements, you may assume that A,...

 

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Each of the statements below is an implication. In these statements, you may assume that A, B, and C are points, and m are lines, and x is a real number, all of which have been previously defined; there are no implicit universal quantifiers in these statements. For each statement, do all of the following: • Identify the hypothesis and the conclusion. • Write the contrapositive. .Write the converse. • Write the negation. Your answers should be written as ordinary (unambiguous) English sentences. Expand the negations as explained in this appendix; don't just write "It is not true that ...." (a) If A, B, and C all lie on l, then they are collinear. (b) If is a line, then it contains at least two distinct points. (c) A quadrilateral is a parallelogram if it is a rectangle. (d) For a triangle to be isosceles, it is necessary that it have two equal angles. (e) x is divisible by 4 only if it is even. (f) If 2x + 1 = 5, then x = 2 or x = 3. Each of the statements below is an implication. In these statements, you may assume that A, B, and C are points, and m are lines, and x is a real number, all of which have been previously defined; there are no implicit universal quantifiers in these statements. For each statement, do all of the following: • Identify the hypothesis and the conclusion. • Write the contrapositive. .Write the converse. • Write the negation. Your answers should be written as ordinary (unambiguous) English sentences. Expand the negations as explained in this appendix; don't just write "It is not true that ...." (a) If A, B, and C all lie on l, then they are collinear. (b) If is a line, then it contains at least two distinct points. (c) A quadrilateral is a parallelogram if it is a rectangle. (d) For a triangle to be isosceles, it is necessary that it have two equal angles. (e) x is divisible by 4 only if it is even. (f) If 2x + 1 = 5, then x = 2 or x = 3.

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PART A Hypothesis A B and C all lie on l Conclusion They are collinear Contrapositive If points are ... View the full answer