Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Need help with True or False for the following... (I will put what I believe As (T) or (F)) 1. For all natural numbers a, a^2 = 0 (mod 4) or a^2 = 1 (mod 4). (T) 2. For all natural numbers a, if a^2 = 2 (mod 4), then 1 = 2. (T) 3. For all natural numbers a, If a^2 = 2 (mod 4), then 1 != 2.  (T) The negation of statement 2, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) or 1 ≠ 2" (F) The negation of statement 3, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) and 1 = 2" (F) The converse of statement 2, which I believe  is "If 1 = 2, then for all natural numbers a, a^2 = 2 (mod 4)" The converse of statement 3, which I believe is "If 1 ≠ 2, then for all natural numbers a, a^2 = 2 (mod 4)" (F) The contrapositive of statement 2, which is "If 1 ≠ 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)" The contrapositive of statement 3, which is "If 1 = 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)" (F) For sets A and B, A = B if and only if A is a subset of B and B is a subset of A.

Need help with True or False for the following... (I will put what I believe As (T) or (F)) 1. For all natural numbers a, a^2 = 0 (mod 4) or a^2 = 1 (mod 4). (T) 2. For all natural numbers a, if a^2 = 2 (mod 4), then 1 = 2. (T) 3. For all natural numbers a, If a^2 = 2 (mod 4), then 1 != 2.  (T) The negation of statement 2, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) or 1 ≠ 2" (F) The negation of statement 3, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) and 1 = 2" (F) The converse of statement 2, which I believe  is "If 1 = 2, then for all natural numbers a, a^2 = 2 (mod 4)" The converse of statement 3, which I believe is "If 1 ≠ 2, then for all natural numbers a, a^2 = 2 (mod 4)" (F) The contrapositive of statement 2, which is "If 1 ≠ 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)" The contrapositive of statement 3, which is "If 1 = 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)" (F) For sets A and B, A = B if and only if A is a subset of B and B is a subset of A.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
See similar textbooks
icon
Related questions
Question

Need help with True or False for the following... (I will put what I believe As (T) or (F))

1. For all natural numbers a, a^2 = 0 (mod 4) or a^2 = 1 (mod 4). (T)

2. For all natural numbers a, if a^2 = 2 (mod 4), then 1 = 2. (T)

3. For all natural numbers a, If a^2 = 2 (mod 4), then 1 != 2.  (T)

The negation of statement 2, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) or 1 ≠ 2" (F)

The negation of statement 3, which I believe is "There exists a natural number a such that a^2 ≠ 2 (mod 4) and 1 = 2" (F)

The converse of statement 2, which I believe  is "If 1 = 2, then for all natural numbers a, a^2 = 2 (mod 4)"

The converse of statement 3, which I believe is "If 1 ≠ 2, then for all natural numbers a, a^2 = 2 (mod 4)" (F)

The contrapositive of statement 2, which is "If 1 ≠ 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)"

The contrapositive of statement 3, which is "If 1 = 2, then there exists a natural number a such that a^2 ≠ 2 (mod 4)" (F)

For sets A and B, A = B if and only if A is a subset of B and B is a subset of A.

Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS