1. Proof the following statement: I a) Let x E R. If x > 0, then x² + 2 > 0 b) Suppose n € Z. If n² < 0, then n is positive or negative number. c) Proof that 5X +3 is even if and only if X is odd.
1. Proof the following statement: I a) Let x E R. If x > 0, then x² + 2 > 0 b) Suppose n € Z. If n² < 0, then n is positive or negative number. c) Proof that 5X +3 is even if and only if X is odd.
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter8: Arrays And Strings
Section: Chapter Questions
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Question
![Tutorial 5 (Methods of Proof)
1. Proof the following statement:
2.
I
a) Let x E R. If x > 0, then x² + 2 > 0
b) Suppose ne Z. If n² <0, then n is positive or negative number.
c) Proof that 5X + 3 is even if and only if X is odd.
d)
Prove the following sentence using Proof by Contradiction technique.
For all real numbers x and y, if x + y >= 2 then either x >= 1 or y >=1.
Let n e Z. Then n²+ 3n +5 is an odd integer (PROOF BY CASES)
B
72
61%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9647fdfe-7af0-4952-a870-5df476c14c0a%2Fbcfa47fc-79d8-49dc-abea-8aff1f83ae1c%2Fxddx2w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Tutorial 5 (Methods of Proof)
1. Proof the following statement:
2.
I
a) Let x E R. If x > 0, then x² + 2 > 0
b) Suppose ne Z. If n² <0, then n is positive or negative number.
c) Proof that 5X + 3 is even if and only if X is odd.
d)
Prove the following sentence using Proof by Contradiction technique.
For all real numbers x and y, if x + y >= 2 then either x >= 1 or y >=1.
Let n e Z. Then n²+ 3n +5 is an odd integer (PROOF BY CASES)
B
72
61%
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