COMP1002 Theory 1
Exercises I: Basic propositional logic.
With answers.
Robin Hirsch
November 26, 2010
Here is the definition of a propositional formula:
proposition::=
p

q

r

p
0

p
1

p
2

. . .
bin
connective::=
∧ ∨  →  ↔
formula ::= proposition
¬
formula

(formula bin
connective formula)
Which of the following are propositional formulas? You should use the definition above quite
rigidly to determine your answer.
1.
p
Answer: yes
2. (
p
→
q
)
Answer: yes
3. (
p
∨
q
∨
r
)
Answer: no — could write
((
p
∨
q
)
∨
r
)
instead though
4.
¬
(
p
)
Answer: no — cannot put brackets round
p
5. (
p
→
(
q
→
p
))
Answer: yes
6.
p
↔
q
Answer: no — brackets needed
7. (
p
↔
q
)
↔
(
p
∨ ¬
q
)
Answer: no — missing outer brackets
Translate the following English sentences into propositional logic, clearly identifying your el
ementary clauses.
Answer: Let
n
=
“I will go”,
p
=
“you will go”,
q
=
“It will
rain soon”,
r
=
“Crop will fail”,
s
=
“I drink too much”,
t
=
“I pass out”,
u
=
“I do something
outrageous”,
v
=
“cats allowed”,
w
=
“dogs allowed”,
x
=
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 Spring '11
 latifa
 Logic, Logical connective, Propositional calculus, valid answer, bin connective formula

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