Practice Proof By Contraposition (10.1.3.1) - Proof Strategies-I - Discrete Mathematics

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is proof by contraposition?
Show hintHide hint
Think about the relationship between P and Q.
Question 2.
If P → Q is true, what can we say about ¬P?
Show hintHide hint
Focus on the logic of implications.
3Question 3.
What does proof by contraposition allow us to do?
- Prove P directly
- Prove ¬Q leads to ¬P
- Confirm P is always true
Show hintHide hint
Focus on the structure of the implication.
4Question 4.
True or False: Vacuous proofs are always useful.
- True
- False
Show hintHide hint
Consider when a premise may easily be false.
Question 5.
Prove by contradiction that √3 is irrational.
Show hintHide hint
Think about the implications of squaring both sides.
Question 6.
Demonstrate using vacuous proof that 'If n > 5, then n^2 > 25' holds true when n = 3.
Show hintHide hint
Evaluate the initial premise.

4 more questions in this section. Enroll free to practise them all.