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Example: Suppose nez. If n² is even, then n is even. Proof (Contrapositive). Suppose n is not even, Then nis odd, so n = 2a + 1 for some integer a by definition of an odd number. Thus n² = (2a+ı) ² 2 = 2 So, n² is odd Therefore n² is PAGE DATE 492 +4a11 = 2 (29²+2a) + 1 + Consequently, n² = (26 + 1)² =1²49²2²4 alretratis where b is integer 20² +29 not even.

Example: Suppose nez. If n² is even, then n is even. Proof (Contrapositive). Suppose n is not even, Then nis odd, so n = 2a + 1 for some integer a by definition of an odd number. Thus n² = (2a+ı) ² 2 = 2 So, n² is odd Therefore n² is PAGE DATE 492 +4a11 = 2 (29²+2a) + 1 + Consequently, n² = (26 + 1)² =1²49²2²4 alretratis where b is integer 20² +29 not even.

Advanced Engineering Mathematics
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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Example: => Suppose nez. If n² is even, then n is even. Proof (Contrapositive). Suppose n is not even, Then n is odd, so n=2a+ 1 for some integer a by definition of an odd number. 2 Thus n² =12a+ı)² PAGE DATE 49² +4a+1 = 2 /29² +2a) + 1 Consequently, n² = (26 + 1)² =²492² 2² teatty where b is integer 20₁² + 20 So, n² is odd Therefore n² is not even. +gate
Transcribed Image Text:Example: => Suppose nez. If n² is even, then n is even. Proof (Contrapositive). Suppose n is not even, Then n is odd, so n=2a+ 1 for some integer a by definition of an odd number. 2 Thus n² =12a+ı)² PAGE DATE 49² +4a+1 = 2 /29² +2a) + 1 Consequently, n² = (26 + 1)² =²492² 2² teatty where b is integer 20₁² + 20 So, n² is odd Therefore n² is not even. +gate
Seatwork 1) Suppose a, b.c. EZ. If a does not divide bc, then a does not divide b. 3 2) Suppose XER. If x²³²_-x>0, then X > -1.
Transcribed Image Text:Seatwork 1) Suppose a, b.c. EZ. If a does not divide bc, then a does not divide b. 3 2) Suppose XER. If x²³²_-x>0, then X > -1.
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