Let & € N. Prove by using the contra-positive that if ³ is odd then x is odd. Proof: Choose the correct starting premise for a proof using the contra-positive: [Select] [Select] If x is even, then x^3 is even If x is even, then x^3 is odd If x^3 is even, then x is even If x^3 is odd, then x odd 2x is even, and hence (2x)^3 is even

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let & € N. Prove by using the contra-positive that if ³ is odd then x is odd.
Proof:
Choose the correct starting premise for a proof using the contra-positive: [Select]
[Select]
If x is even, then x^3 is even
If x is even, then x^3 is odd
If x^3 is even, then x is even
If x^3 is odd, then x odd
2x is even, and hence (2x)^3 is even
Transcribed Image Text:Let & € N. Prove by using the contra-positive that if ³ is odd then x is odd. Proof: Choose the correct starting premise for a proof using the contra-positive: [Select] [Select] If x is even, then x^3 is even If x is even, then x^3 is odd If x^3 is even, then x is even If x^3 is odd, then x odd 2x is even, and hence (2x)^3 is even
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