Unit 5 Exercises
1. Use truth table to verify the following equivalences.
a) p F F
b) p T T
c) p p p
2. Use truth tables to verify the distributive law p (q r) (p q) (p r).
3. Show that each of the following implications is a tautology without using truth tables.
a) p (p q)
b) (p q) (p q)
c) (p q) q
4. Verify the following equivalences, which are known as the absorption laws.
a) [ p (p q) ] p
b) [ p (p q) ] p
5. Find the dual of each of the following propostions.
6. Find a compound proposition involving the propositions p,q, and r that is true when exactly one of p, q, and ris true and is false otherwise. (Hint: Form a disjunction of conjunctions. Include a conjunction for each combination of values for which the propostion istrue. Each conjunction should include each of the three propositions or theirnegations.)
Answers for these exercises