Use the definitions to show that the following statements are true. For example, to show that 5 | 20, we could state that 20 = 5(4), and since 4 is an integer, 5 | 20 (by the definition of “divides”). (a) 8 | (−56) (b) 17 | 0 (c) 33 is a multiple of 11. (d) 12 is a divisor of 192. (e) (∃p ∈ Z) ((p | 7) ∧ (p | 4)) (f) (∃q ∈ Z) ((7 | q) ∧ (4 | q)) (g) (∃p, q ∈ Z) ((p 6= q) ∧ ((p | q) ∧ (q | p)))
Use the definitions to show that the following statements are true. For example, to show that 5 | 20, we could state that 20 = 5(4), and since 4 is an integer, 5 | 20 (by the definition of “divides”). (a) 8 | (−56) (b) 17 | 0 (c) 33 is a multiple of 11. (d) 12 is a divisor of 192. (e) (∃p ∈ Z) ((p | 7) ∧ (p | 4)) (f) (∃q ∈ Z) ((7 | q) ∧ (4 | q)) (g) (∃p, q ∈ Z) ((p 6= q) ∧ ((p | q) ∧ (q | p)))
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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Question
Use the definitions to show that the following statements
are true.
For example, to show that 5 | 20, we could state that 20 = 5(4), and since 4 is an integer, 5 | 20 (by the definition of “divides”).
(a) 8 | (−56)
(b) 17 | 0
(c) 33 is a multiple of 11.
(d) 12 is a divisor of 192.
(e) (∃p ∈ Z) ((p | 7) ∧ (p | 4))
(f) (∃q ∈ Z) ((7 | q) ∧ (4 | q))
(g) (∃p, q ∈ Z) ((p 6= q) ∧ ((p | q) ∧ (q | p)))
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