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Math 266, Quiz #1, Summer 2010
Name _______________________________________________
Instructions: Show all work. On proofs, clearly explain your reasoning. Unexplained leaps of logic, even
if correct, will be treated as if it is false. On take home quizzes, all work must be your own; you may not
work together.
1. How many rows appear in a truth table for each of these compound propositions?
a. ( q  p )  (p  q)
4
b.
( p  t )  ( p  s )
c.
( p  r )  (s  t )  (u  v )
64
d.
( p  r  s )  ( q  t )  ( r  t )
32
8
2. Construct a truth table for the proposition ( p  q)  ( p  q) . You may use the table below,
though you may not need the whole table. If you need additional paper, ask.
p
( p  q)
q
( p  q)
( p  q)  ( p  q)
T
T
T
T
T
T
F
T
F
F
F
T
T
F
F
F
F
F
F
T
3. Determine the truth value of each of these statements if the domain consists of all real
numbers.
a.
x( x 3  1)
b.
x( x  x )
c.
x(( x)  x )
4
T
2
2
d. x (2 x  x )
T
2
F
F
4. Use a truth table to show that p  q and ( p  q)  ( q  p ) are logically equivalent.
p
pq
q
( p  q)
(q  p)
( p  q)  ( q  p )
T
T
T
T
T
T
T
F
F
F
T
F
F
T
F
T
F
F
F
F
T
T
T
T
5. Find a counterexample, if possible, to these universally quantified statements, where the
domain for all variables consists of all real numbers.
a.
x( x 2  x )
b. x( x  0  x  0)
c.
x ( x  1)
x=1,x=0
x=0
x=2, any number not =1