25. Let Q : N → {true, false} be a predicate with domain the natural numbers N = {0, 1, 2, . . .} and defined by the statement Q(k) = “k is a prime number”. Identify the following propositions as true or false. Unless otherwise stated, only use. • the fact that the only even prime is 2, and
25. Let Q : N → {true, false} be a predicate with domain the natural numbers N = {0, 1, 2, . . .} and defined by the statement Q(k) = “k is a prime number”. Identify the following propositions as true or false. Unless otherwise stated, only use. • the fact that the only even prime is 2, and
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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25. Let Q : N → {true, false} be a predicate with domain the natural numbers N =
{0, 1, 2, . . .} and defined by the statement Q(k) = “k is a prime number”. Identify the
following propositions as true or false. Unless otherwise stated, only use.
• the fact that the only even prime is 2, and
• basic arithmetic with natural numbers.
Show all you working and reasoning.
(a) Q(1), Q(2), Q(3), Q(4)
(b) For all k ∈ N, k > 2, we have ¬Q(k) ∨ ¬Q(k + 3).
(c) ∃k ∈ N : Q(2k)
(d) There exists a k ∈ N such that for all ℓ > k we have that Q(ℓ) is false. You may
use external sources to prove that the proposition is true or false.
Can you please help me to show working out for the question 25? Thank you
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