Week 1

Question 1

What is the definition of a statement in mathematics?

Answer 1

A statement is a sentence that is always true or always false.

Question 2

What is an implication statement?

Answer 2

A implies B. If A is true then B is true, otherwise B is false. A->B

Question 3

What is a compound statement?

Answer 3

A combination of two or more statements to communicate a larger statement.

Question 4

What is the double negation property of statements?

Answer 4

Neg(Neg A) = A

Question 5

What are the De Morgan Laws of statements?

Answer 5

Neg(A and B) = Neg A or Neg B
Neg(A or B) = Neg A and Neg B

Question 6

What are the distributivity laws of statements?

Answer 6

A and (B or C) = (A and B) or (A and C)
A or (B and C) = (A or B) and (A or C)

Question 7

What are contrapositive statements?

Answer 7

A -> B = neg(B) -> neg(A)

Question 8

What are converse statements?

Answer 8

A -> B = B -> A

Question 9

What is equivalence as double implication?

Answer 9

(A = B) = (A -> B) and (B -> A)

Question 10

What is a direct proof?

Answer 10

Using a logical sequence of statements to show a statement is true/false. Use both maths and sentences.

Question 11

What is a proof by contraposition?

Answer 11

Prove that A implies B by proving neg B implies neg A.

Question 12

What is a proof by contradiction?

Answer 12

Start by assuming the opposite of the statement is true. Work through proving that the opposite is true until you get to a contradiction.

Question 13

What is the definition of an even number?

Answer 13

n = 2a where a is an integer

Question 14

What is the definition of an odd number?

Answer 14

n = 2a + 1 where a is an integer