Practice Question 3 (6.4) - Tutorial 1: Part I - Discrete Mathematics

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6 sample questions

Question 1.
Create a truth table for the proposition p → q.
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Remember to note when `p` being true and `q` being false is the only situation that makes `p → q` false.
Question 2.
What does ¬ p represent?
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Think of it as 'not p'.
3Question 3.
What is the only situation where p → q is false?
- When both are true
- When `p` is true and `q` is false
- When both are false
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Think about the conditional relationship.
4Question 4.
Is p ↔ q true if both p and q are false?
- True
- False
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Consider the definition of bi-implication.
Question 5.
Construct a complete truth table for the expression ((p → q) ∧ (¬ p → r)) ↔ (q ∨ r).
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Check each part incrementally, ensuring you're capturing the implications accurately.
Question 6.
Prove using truth values that (p → q) -> (¬ q → ¬ p) is a tautology.
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Focus on filling out the truth values for both sides and comparing.

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