Notes on Logic and Proof

Question 1

What is a statement

Answer 1

• a sentence which is definitely true or definitely false
• can never be both true and false

Question 2

Truth value of a statement

Answer 2

Whether the statement is true or false

Question 3

If two statements are ‘logically equivalent’

Answer 3

The two statements have the same truth values in the same circumstances

Question 4

What does not A or B mean?

Answer 4

• (not A) or B
• different from not (A or B)

Question 5

What does ‘A or B’ mean

Answer 5

Either A is true, or B is true, or both are true

Question 6

If A then B

Answer 6

If A is true then B bust also be true

Question 7

If 0 = 1, then 2 + 2 = 5
Is this a true or false statement?

Answer 7

True because A is false and B is false

Question 8

Converse of ‘if A then B’

Answer 8

If B then A

Question 9

Converse of ‘A only if B’

Answer 9

B only if A

Question 10

Contrapositive of ‘if A then B’

Answer 10

If not B then not A

Question 11

Contrapositive of ‘A only if B’

Answer 11

Not B only if not A

Question 12

Contrapositive of ‘A iff B’

Answer 12

Not B iff not A

Question 13

‘A is sufficient for B’ arrows

Answer 13

A -> B

Question 14

‘A is necessary for B’ arrows

Answer 14

A <- B

Question 15

‘A is necessary and sufficient for B’ arrows

Answer 15

A <=> B