ADDITIONAL RULES FOR PROOFS

Question 1

Describe Disjunctive Syllogism (DS).

Answer 1

If either A or B is true, and A is false, then B must be true.

Question 2

Explain Modus Tollens (MT).

Answer 2

If A implies B, and B is false, then A must also be false.

Question 3

Give an example of Modus tollens (MT).

Answer 3

If A is ‘If she won, she’s in the White House’ and ¬B is ‘She’s not in the White House’, then the conclusion is ‘She didn’t win’.

Question 4

Define Double-Negation Elimination (DNE).

Answer 4

Not-not A is just A.

Question 5

Illustrate Double-Negation Elimination (DNE) with an example.

Answer 5

If ¬¬A is ‘It’s not true that she’s not happy’, then the conclusion is ‘She is happy’.

Question 6

What does the Law of Excluded Middle (LEM) state?

Answer 6

A is either true or false, with no middle ground.

Question 7

Provide an example of the Law of Excluded Middle (LEM).

Answer 7

Either it’s sunny, or it’s not sunny. There is no third option.

Question 8

Explain De Morgan’s Laws in the context of negation.

Answer 8

Not (A and B) is the same as Not A or Not B, and Not (A or B) is the same as Not A and Not B.

Question 9

Give an example of De Morgan’s Laws for negating AND.

Answer 9

¬(A∧B) is equivalent to ¬A∨¬B: If it’s not both raining and sunny, it’s either not raining or not sunny.

Question 10

Give an example of De Morgan’s Laws for negating OR.

Answer 10

¬(A∨B) is equivalent to ¬A∧¬B: If it’s not raining or sunny, it’s neither raining nor sunny.