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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define tautology and give an example.
💡 Hint: Think of a statement that cannot be false.
Question 2
Easy
What is a contradiction? Give an example.
💡 Hint: Consider how you can have p true and false simultaneously.
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 do we call a statement that is always true?
- A) Tautology
- B) Contradiction
- C) Contingency
💡 Hint: This type of statement includes `p ∨ ¬p`.
Question 2
Is p ∧ ¬p a tautology?
- True
- False
💡 Hint: What happens when p takes both true and false values?
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using De Morgan's laws, prove that ¬(p ∧ q) is logically equivalent to ¬p ∨ ¬q. Include all logical steps.
💡 Hint: Consider how negation would affect both components.
Question 2
Create a complex logical statement involving multiple variables and use logical identities to simplify and demonstrate equivalence.
💡 Hint: Think of separating the conjunction over the disjunction and applying negation effectively.
Challenge and get performance evaluation