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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 35E

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