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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a tautology is and give an example.
💡 Hint: Think of statements that cannot be false.
Question 2
Easy
What does the statement 'p if and only if q' represent?
💡 Hint: Consider when both statements hold the same truth values.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the definition of logical equivalence?
- A condition where two propositions always yield the same truth value.
- A statement that is occasionally true.
- Two propositions can never be false.
💡 Hint: Think of the relationship between truth values.
Question 2
True or False: A contradiction is a statement that is always true.
- True
- False
💡 Hint: Consider its definition.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that (p → q) and ¬(p ∧ ¬q) are logically equivalent using any logical identities.
💡 Hint: Start with rewriting one statement and use identities.
Question 2
Use truth tables to establish the equivalence of (p ∨ q) and ¬(¬p ∧ ¬q).
💡 Hint: Outline all possibilities for p and q.
Challenge and get performance evaluation