Unit 5 Sections 5-1 to 5-5

Question 1

Inverse?

Answer 1

Negate both the hypothesis and conclusion.
May have a different truth value than the original conditional.

Question 2

Contrapositive?

Answer 2

Switches the hypothesis and conclusion and negates both. Always has the same truth value as the original conditional.

Question 3

Converse?

Answer 3

Switches the hypothesis and conclusion. May have the same truth value as the original.

Question 4

Negation?

Answer 4

The negation of a conditional has the opposite truth value as the conditional.

Question 5

Indirect proof steps?

Answer 5

1. Assume the negation of the “Prove” statement
2. Reason logically to show that the assumption leads to a contradiction of a known fact (3 p’s and a d)
3. Conclude the assumption is false and that the “Prove” statement is true; As part of your proof, the last statement, must be:
   “Therefore, the fill in your assumption is false and fill in the prove must be true”

Question 6

What form are indirect proofs done in?

Answer 6

Indirect proofs are done in paragraph form, but must still have statements and reasons as part of the proof.

Question 7

When do two statements contradict each other?

Answer 7

Two statements contradict each other when they cannot both be true at the same time.