Discret Mathmatic \"If n is an even integer, then n + 1 is odd\" Assumption in E

ID: 3142210 • Letter: D

Question

Discret Mathmatic

"If n is an even integer, then n + 1 is odd"

Assumption in English n is even

Assumption in Logic n = 2k

Arithmetic using assumption and leading to conclusion n +1 = 2k + 1

Conclusion n + 1 is odd

Questions

1) Give a proof of the same statement by Contraposition.

Assumption in English =

Assumption in Logic =

Arithmetic using assumption and leading to conclusion =

Conclusion =

2) Give a proof of the same statement by Contradiction.

Assumption in English =

Assumption in Logic =

Arithmetic using assumption and leading to conclusion =

Conclusion =

1) Give a proof of the same statement by Contraposition.

Assumption in English = n+1 is even

Assumption in Logic = n+1 = 2k

Arithmetic using assumption and leading to conclusion = n = 2k-1

Conclusion = n is odd

2) Give a proof of the same statement by Contradiction.

Assumption in English = n is even and n+1 is even

Assumption in Logic = n = 2k and n+1 = 2r

Arithmetic using assumption and leading to conclusion = (n+1) - 1 = 2r - 2k => 1 = 2 (r-k) => 2 | 1

Conclusion = n+1 is odd

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