Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.3 - Page 130: 21

Answer

(a) TRUE; 2x + y =7 . (B) THE GIVEN STATEMENT IS TRUE (C) ALSO THE THIRD STATEMENT IS TRUE (D) CLEARY THE EQUATION HOLDS. (E) THIS STATEMENT IS FALSE FOR BOTH X AND Y.

Work Step by Step

(a) TRUE; 2x + y =7 . GIVE ANY VALUE TO X THERE EXISTS A VALUE OF Y SO THAT GIVEN EQUATION HOLDS. (B) THE GIVEN STATEMENT IS TRUE (C) ALSO THE THIRD STATEMENT IS TRUE FOR BOTH X AND Y.GIVEN ANY VALUE TO X, THE SAME VALUE FOR Y SATISFIES THE GIVEN EQUATION (D) CLEARY THE EQUATION HOLDS. GIVE ANY VALUE TO X THERE EXISTS A VALUE OF Y=1 WHICH SATISFIES THE GIVEN EQUATION.SIMILARLY, GIVE ANY VALUE TOY THERE EXISTS A VALUE OF X=5 WHICH SATISFIES THE GIVEN EQUATION (E) THIS STATEMENT IS FALSE FOR BOTH X AND Y. BECAUSE IF WE GIVE ANY VALUE TO X THERE EXISTS AN IMAGINARY VALUE OF Y WHICH SATISFIES THE GIVEN EQUATION. THUS THERE DOES NOT EXIST A REAL NO.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.