F 
FUnit 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.
q
r
q
r)
s F)
(q
T)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.)