Try It Now

Work these exercises to see how well you understand this material.

Exercises

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

  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 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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