Advanced Math 4.14 (1,3,6), 4.15 (3,4) Problem 4.14. Write the following mathematical statements using only symbols. Are the statements true? (1) 3 divides 9. (2) 2 and 3 are divisors of 12. (3) Every real number is positive. (4) Any number divides its square. (5) 1 divides any number. (6) Every number divides zero. An answer to (2) is 2 12 / 3|12; true. We say that a number n is even if 2|n, and n is odd if 3m, n = m + 1 and m is even. Equivalently, n-1 is even. A natural number p is prime iff its only divisors are 1 and itself and p 1. For example, 2, 3, 7 are prime. More formally, p is prime if and only if p1^Vd, (dpd=1vd=p). Problem 4.15. Write the following mathematical statements using only symbols. Are the statements true? (1) 5 is an odd number. (2) Any integer is even or odd. (3) The square of an odd number is odd. (4) 9 is a prime number. An answer to (1) is 3c, 2c + 1 = 5; true.
Advanced Math 4.14 (1,3,6), 4.15 (3,4) Problem 4.14. Write the following mathematical statements using only symbols. Are the statements true? (1) 3 divides 9. (2) 2 and 3 are divisors of 12. (3) Every real number is positive. (4) Any number divides its square. (5) 1 divides any number. (6) Every number divides zero. An answer to (2) is 2 12 / 3|12; true. We say that a number n is even if 2|n, and n is odd if 3m, n = m + 1 and m is even. Equivalently, n-1 is even. A natural number p is prime iff its only divisors are 1 and itself and p 1. For example, 2, 3, 7 are prime. More formally, p is prime if and only if p1^Vd, (dpd=1vd=p). Problem 4.15. Write the following mathematical statements using only symbols. Are the statements true? (1) 5 is an odd number. (2) Any integer is even or odd. (3) The square of an odd number is odd. (4) 9 is a prime number. An answer to (1) is 3c, 2c + 1 = 5; true.
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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Plz solve part 1.3.6 from 4.14 and part 3.4 from 4.15 within 30 minutes
Transcribed Image Text:Advanced Math
4.14 (1,3,6), 4.15 (3,4)
Problem 4.14. Write the following mathematical statements using only
symbols. Are the statements true?
(1) 3 divides 9.
(2) 2 and 3 are divisors of 12.
(3) Every real number is positive.
(4) Any number divides its square.
(5) 1 divides any number.
(6) Every number divides zero.
An answer to (2) is 2 12 / 3|12; true.
We say that a number n is even if 2|n, and n is odd if 3m, n = m + 1
and m is even. Equivalently, n-1 is even. A natural number p is prime
iff its only divisors are 1 and itself and p 1. For example, 2, 3, 7 are
prime. More formally, p is prime if and only if
p/1/d, (dpd=1vd=p).
Problem 4.15. Write the following mathematical statements using only
symbols. Are the statements true?
(1) 5 is an odd number.
(2) Any integer is even or odd.
(3) The square of an odd number is odd.
(4) 9 is a prime number.
An answer to (1) is 3c, 2c + 1 = 5; true.
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