Practice Logical Equivalence (2.1) - Logical Equivalence - Discrete Mathematics

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8 questions

Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define what a tautology is and give an example.
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Think of statements that cannot be false.
Question 2.
What does the statement 'p if and only if q' represent?
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Consider when both statements hold the same truth values.
3Question 3.
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.
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Think of the relationship between truth values.
4Question 4.
True or False: A contradiction is a statement that is always true.
- True
- False
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Consider its definition.
Question 5.
Prove that (p → q) and ¬(p ∧ ¬q) are logically equivalent using any logical identities.
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Start with rewriting one statement and use identities.
Question 6.
Use truth tables to establish the equivalence of (p ∨ q) and ¬(¬p ∧ ¬q).
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Outline all possibilities for p and q.

4 more questions in this section. Enroll free to practise them all.