MAT2051 Discrete Mathematics LATEST EXAM w/ RATIONALES 2026 Complete And Verified Study material) (22pages) LEARNEXAMS

https://shop.4studentbooks.shop/downloads/test-bank-solution-manual-for-understanding-icd-10-cm-and-icd-10-pcs-a-worktext-2026-edition-9th-ePART A:

1. Consider the following proposition: "For all natural

numbers n, if n is even, then n + 1 is odd." Which of the

following is a valid way to prove this proposition by

contradiction?

a) Assume that there exists a natural number n such that n is

even and n + 1 is even, and derive a contradiction.

b) Assume that there exists a natural number n such that n is

odd and n + 1 is odd, and derive a contradiction.

c) Assume that for all natural numbers n, n is even and n + 1

is even, and derive a contradiction.

d) Assume that for all natural numbers n, n is odd and n + 1

is odd, and derive a contradiction.

*Answer: a) This is the correct way to prove the proposition

by contradiction. If we assume that there exists a natural

number n such that n is even and n + 1 is even, then we can

write n = 2k and n + 1 = 2l for some natural numbers k and

l. But then we have 2l - 2k = 1, which implies that 1 is

divisible by 2, which is a contradiction.*

2. Consider the following relation R on the set {a, b, c, d}:

R = {(a, a), (a, b), (b, b), (b, c), (c, c), (c, d), (d, d)}. Which

of the following statements are true about R?

a) R is reflexive

b) R is symmetric

c) R is transitive

d) R is antisymmetric

*Answer: a) and c) R is reflexive because for every element dition-by-mary-jo-bowie/