Consider the proposition ∀x ∈ R, if x 2 is irrational then x is irrational. Write down the contrapositive and try to prove it (you may take it as given that the product of two integers is also an integer)
Consider the proposition ∀x ∈ R, if x 2 is irrational then x is irrational. Write down the contrapositive and try to prove it (you may take it as given that the product of two integers is also an integer)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Consider the proposition ∀x ∈ R, if x 2 is irrational then x is irrational. Write down
the contrapositive and try to prove it (you may take it as given that the product of
two integers is also an integer).
Expert Solution
Step 1
The given statement is , if is irrational then x is irrational. Prove using the contrapositive method. To prove the given statement, prove that , if x is not irrational then is not irrational.
Consider x is not irrational and is irrational.
Therefore x is rational, therefore, where and .
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