Practice Summary Of Concepts Introduced (2.6.1) - Logical Equivalence - Discrete Mathematics - Vol 1
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Summary of Concepts Introduced

Practice - Summary of Concepts Introduced

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a tautology? Give an example.

💡 Hint: Think of statements that cover all truth values.

Question 2 Easy

Define a contradiction and give an example.

💡 Hint: Look for examples where one part conflicts with another.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following is always true?

p ∧ ¬p
p ∨ ¬p
p → ¬p

💡 Hint: Consider what happens if p is true or false.

Question 2

Is p → q equivalent to ¬q → ¬p?

True
False

💡 Hint: Think of the meaning of each side of the equivalence.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the statements p = 'It rains' and q = 'The ground is wet'. Show using logical equivalence that 'If it does not rain, then the ground is not wet' is equivalent to 'If the ground is wet, then it has rained'.

💡 Hint: Start with rewriting the statements using known identities.

Challenge 2 Hard

Using De Morgan's Law, simplify ¬(p ∨ q).

💡 Hint: Focus on how negation interacts with conjunctions and disjunctions.

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