Analysis 1: Exercises 1
1.
Identify the premises and conclusions of the following deductive arguments and
analyse their logical form. Do you think the reasoning is valid? Just use your intuition
for now.
(a) The main course will be either beef or ﬁsh. The vegetable will be either peas or
corn. We will not have both ﬁsh as a main course and corn as a vegetable.
Therefore, we will not have both beef as a main course and peas as a vegetable.
(b) Either sales will go up and the boss will be happy, or expenses will go up and the
boss won’t be happy. Therefore, sales and expenses will not both go up.
2.
In this exercise we will use the symbol + to mean
exclusive or
. In other words,
P
+
Q
means ”P or Q, but not both”.
(a) Make a truth table for
P
+
Q
.
(b) Find a formula using only the connectives
∧
,
∨
and
¬
that has the same truth
table as
P
+
Q
.
3.
Find a formula involving the connectives
∧
,
∨
and
¬
that has the following truth table:
P
Q
???
F
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 Winter '10
 Spyros
 Logic, Johns, Main course, following propositional forms

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