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

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6 sample questions

Question 1.
What is a tautology? Give an example.
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Think of statements that cover all truth values.
Question 2.
Define a contradiction and give an example.
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Look for examples where one part conflicts with another.
3Question 3.
Which of the following is always true?
- p ∧ ¬p
- p ∨ ¬p
- p → ¬p
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Consider what happens if p is true or false.
4Question 4.
Is p → q equivalent to ¬q → ¬p?
- True
- False
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Think of the meaning of each side of the equivalence.
Question 5.
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'.
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Start with rewriting the statements using known identities.
Question 6.
Using De Morgan's Law, simplify ¬(p ∨ q).
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Focus on how negation interacts with conjunctions and disjunctions.

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