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
icon
Related questions
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 xR, if x2 is irrational then x is irrational. Prove using the contrapositive method. To prove the given statement, prove that xR, if x is not irrational then x2 is not irrational.

Consider x is not irrational and x2 is irrational.

Therefore x is rational, therefore, x=pqwhere gcdp,q=1 and q0.

 

 

 

 

 

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,