Quiz Step by Step 2. Mathematics - Advanced Math

1

Free

True or false? For any irrational number r, r2 is irrational. Justify your answer.

2

Free

Consider the following statement: For all integers n, if n^3 is odd then n is odd.

3

Free

Consider the following statement: For all real numbers r, if r^3 is irrational then r is irrational.

4

Free

Consider the following statement: For all integers n, if n^3 is even then n is even.

5

Free

Prove the following statement by contradiction: For all real numbers r and s, if r is rational and s is irrational, then r + 2s is irrational.

6

Prove the following statement: There is no smallest positive rational number.

7

Prove the following statement: For all real numbers x, [x − 2] = [x] − 2.

8

Prove the following statement: The sum of any two consecutive integers can be written in the form 4n + 1 for some integer n.

9

Prove the statement below directly from the definitions of the terms. Do not use any other facts previously proved in class or in the text or in the exercises.

10

Prove the following statement directly from the definition of divisibility. Do not use any other facts previously proved in class or in the text or in the exercises.For all integers a, and b, if a divides b then a^3 divides b^3.

11

Prove the following statement directly from the definitions of the terms. Do not use any other facts previously proved in class or in the text or in the exercises.

12

Prove the following statement directly from the definitions of the terms. Do not use any other facts previously proved in class or in the text or in the exercises

13

Outline a proof of the following statement by writing the “starting point” and the “conclusion to be shown” in a proof of the statement.

14

Does 12 divide 72? Justify your answer.

15

Is 0 divisible by 3? Justify your answer.

16

State precisely (but concisely) what it means for an integer n to be divisible by an integer d.

17

Is 56.745 a rational number? Justify your answer.

18

Is 605.83 a rational number? Justify your answer.

19

State precisely (but concisely) what it means for a number r to be rational.

20

Show that the following statement is false: The product of any two irrational numbers is irrational.

21

If m and n are integers, is 6m2 + 34n − 18 an even integer? Justify your answer.

22

Consider the following statement:

23

Find a counterexample to show that the following statement is false:

24

State precisely (but concisely) what it means for an integer n to be odd.

25

Is the following argument valid or invalid? Justify your answer.

26

Is the following argument valid or invalid? Justify your answer.

27

For each of the following statements, (1) write the statement informally without using variables or the symbols ∀ or ∃, and (2) indicate whether the statement is true or false and briefly justify your answer.

28

For each of the following statements, (1) write the statement informally without using variables or the symbols ∀ or ∃, and (2) indicate whether the statement is true or false and briefly justify your answer.

29

Are the following two statements logically equivalent? Justify your answer.

Find your answers, solutions and more...

We made it much easier for you to find exactly what you're looking for on Quizgoat.

Quiz Step by Step 2. Mathematics - Advanced Math

Recent Packs