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MATH 290 – EXAM 1 – SOLUTIONS
Answer all of the following questions on the answer sheets provided. Show all work, as
partial credit may be given. This test will be counted out of a total of 60 points.
1. (8 pts.) Prove that
P
=
⇒
(
Q
∨
R
) is equivalent to (
P
∧ ∼
Q
) =
⇒
R
by ﬁlling in the truth
table below.
P
Q
R
Q
∨
R
P
=
⇒
(
Q
∨
R
)
P
∧ ∼
Q
(
P
∧ ∼
Q
) =
⇒
R
T
T
T
T
T
F
T
T
T
F
T
T
F
T
T
F
T
T
T
T
T
T
F
F
F
F
T
F
F
T
T
T
T
F
T
F
T
F
T
T
F
T
F
F
T
T
T
F
T
F
F
F
F
T
F
T
2. (8 pts. each) Consider the statement:
If
a
+
b
is even, then both
a
and
b
are even or both
a
and
b
are odd.
(a) Translate the above statement into symbolic form.
(b) Identify the antecedent and consequent of the statement.
(c) State in English the converse of the statement.
(d) State in English the contrapositive of the statement.
Solution:
(a) (
a
+
b even
) =
⇒
([(
a even
)
∧
(
b even
)]
∨
[(
a odd
)
∧
(
b odd
)]).
(b) The antecedent of the above implication is (
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 Fall '08
 Alligood,K
 Math, Advanced Math

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