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Try It Now

Exercises

  1. Given the following propositions generated by p, q, and r, which are equivalent to one another?
    1. (p ∧ r) ∨ q
    2. p ∨ (r ∨ q)
    3. r ∧ p
    4. ¬r ∨ p
    5. (p ∨ q) ∧ (r ∨ q)
    6. r → p
    7. r ∨ ¬p
    8. p → r

  2. Is an implication equivalent to its converse? Verify your answer using a truth table.

  3. How large is the largest set of propositions generated by p and q with the property that no two elements are equivalent?

  4. Explain why a contradiction implies any proposition and any proposition implies a tautology.


Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
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