Explanation Given: The given statement “ ∀ x ∈ R , if x ( x + 1 ) < 0 then x < − 1 or x > 0 ” The given statement is true, since if x ( x + 1 ) < 0 then x < − 1 or x > 0 Contrapositive: ∀ x ∈ R , if x ≥ − 1 or x ≤ 0 then x ( x + 1 ) ≤ 0 which is also a true statement, because if x ≥ − 1 or x ≤ 0 ⇒ x ∈ [ − 1 , 0 ] then x ( x + 1 ) ≤ 0 This can be verified by graph also, the is graph of x ( x + 1 ) is given by From the above graph, we can observe that if x ∈ [ − 1 , 0 ] then x ( x + 1 ) ≤ 0

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ISBN: 9780357097717

Author: EPP

Publisher: CENGAGE L

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Chapter 3.2, Problem 28ES

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The contrapositive, converse, and inverse of the given statement“ ∀x∈R, if x(x+1)<0 then x<−1 or x>0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

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The contrapositive, converse, and inverse of the given statement“ ∀ x ∈ R , if x ( x + 1 ) < 0 then x < − 1 or x > 0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

Solution Summary: The author explains the contrapositive, converse, and inverse statements of forall xin R, which are true and false.

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To write:

The contrapositive, converse, and inverse of the given statement“ ∀x∈R, if x(x+1)<0 then x<−1 or x>0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

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The contrapositive, converse, and inverse of the given statement“ ∀ x ∈ R , if x ( x + 1 ) &lt; 0 then x &lt; − 1 or x &gt; 0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

Solution Summary: The author explains the contrapositive, converse, and inverse statements of forall xin R, which are true and false.

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To write: The contrapositive, converse, and inverse of the given statement“ ∀x∈R, if x(x+1)<0 then x<−1 or x>0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

Chapter 3 Solutions

The contrapositive, converse, and inverse of the given statement“ ∀ x ∈ R , if x ( x + 1 ) < 0 then x < − 1 or x > 0 ” .which of these statements are true and which are false. Give a counter example for each that is false.

To write:

The contrapositive, converse, and inverse of the given statement“ ∀x∈R, if x(x+1)<0 then x<−1 or x>0 ” .which of these statements are true and which are false. Give a counter example for each that is false.