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28 Νοε 2020 · Example \(\PageIndex{1}\) If \(n>2\), then \(n^{2}>4\). Find the converse, inverse, and contrapositive. Determine if each resulting statement is true or false. If it is false, find a counterexample. Solution. The original statement is true. \(\underline{Converse}\): If \(n^{2}>4\), then \(n>2\). False. If \(n^{2}=9\), \(n=−3\: or \: 3 ...
18 Ιουλ 2012 · 1. Use the statement: If n> 2, then n2> 4. a) Find the converse, inverse, and contrapositive. b) Determine if the statements from part a are true or false. If they are false, find a counterexample. The original statement is true. Converse _: If n2> 4, then n> 2. False. n could be − 3, making n2 = 9. Inverse _: If n <2, then n2 <4.
5 ημέρες πριν · Examples. Example 1. If n> 2, then n 2> 4. Find the converse, inverse, and contrapositive. Determine if each resulting statement is true or false. If it is false, find a counterexample. The original statement is true. Converse _: If n 2> 4, then n> 2. F a l s e. If n 2 = 9, n = − 3 or 3. (− 3) 2 = 9 Inverse _: If n ≤ 2, then n 2 ≤ 4. F a l s e.
IXL - Converses, inverses, and contrapositives (Geometry practice) Improve your math knowledge with free questions in "Converses, inverses, and contrapositives" and thousands of other math skills.
3 Αυγ 2024 · The converse of the conditional statement is “If Q then P.”. The contrapositive of the conditional statement is “If not Q then not P.”. The inverse of the conditional statement is “If not P then not Q.”. We will see how these statements work with an example.
Inverse: The inverse of a conditional statement “If P, then Q” (P → Q) is the statement “If not P, then not Q” (~P → ~Q). The inverse has the same truth value as the original statement only when the antecedent and consequent have the same truth value.
These new conditionals are called the inverse, the converse, and the contrapositive. Definition of inverse : Inverse is a statement formed by negating the hypothesis and conclusion of the original conditional.
