In each part following is an implication: a statement of the form \"If P then Q.

Question

In each part following is an implication: a statement of the form "If P then Q." In each part, first write the converse and the contrapositive of the given implication. Then label each of the three statements as true or false; no need to prove anything.

(a) If x then x2 > 9.

(b) If x then x - 4x2 + 3x > 0

(c) if a > 0 then b > 0 then |a + b| = |a| + |b|.

Explanation / Answer

Suppose we have a statement if p then q. The converse is If q then p. The Contrapositive is if not q then not p. Using this, we can answer the following questions. a) Converse: If x^2 > 9 then x. Contrapositive: If x^2 0 then x. Contrapositive: If x-4x^2 +3x 0, b > 0. Contrapositive: If |a+b| does not equal |a|+|b| then a

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