Practice Example Of Logical Equivalence Proof (2.5)

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6 sample questions

Question 1.
Define tautology and provide an example.
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Think of an expression that yields true regardless of p’s value.
Question 2.
What does logical equivalence mean?
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Consider statements with identical outcomes.
3Question 3.
What is the definition of logical equivalence?
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Think about identical outcomes in different expressions.
4Question 4.
A statement that is always true is called a?
- Contradiction
- Tautology
- Contingency
- None of these
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Consider an example that never changes its outcome.
Question 5.
Prove that (p ∧ q) → r is logically equivalent to ¬(p ∧ q) ∨ r using logical identities.
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Break down the statement systematically, applying identities.
Question 6.
Show that ¬(p ∨ q) is equivalent to ¬p ∧ ¬q, using De Morgan's Law.
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Negation is key in switching from disjunction to conjunction.

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