Practice Distributive Law (2.3.3) - Logical Equivalence - Discrete Mathematics

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6 sample questions

Question 1.
Define logical equivalence.
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Think about the truth values they represent.
Question 2.
What is a tautology?
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Recall examples like 'p or not p'.
3Question 3.
What does the Distributive Law state?
- A. p and (q or r) = (p and q) or (p and r)
- B. p or (q and r) = (p or q) and (p or r)
- C. Neither A nor B
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Consider how conjunction behaves with operators.
4Question 4.
Is (p and -p) a contradiction?
- True
- False
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Remember the definition of contradiction.
Question 5.
Demonstrate the steps to prove that p and (q or r) simplifies logically to (p and q) or (p and r) using truth tables, and explain each step.
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Detailed tracking of truth values is key.
Question 6.
Given the expression p or (q and r), transform and prove it equivalent to (p or q) and (p or r) using the Distributive Law.
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Breaking down each piece helps in clarity.

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