EXERCISES
1. Which of the following sentences are propositions? What are the truth
values of those that are propositions?
(a) x + y = y + x for every pair of real numbers x and y
(b) Answer this question
(c) y + 2 = 17
(d) 7 + 5 = 10
(e) 3 + 2 = 5
(f) Bombay is the capital of India.
(g) ISPEX is in love with ‘L’JALAJABATVMU
2. Write the negation of each of the following propositions?
(a) Summer in Kodaikanal is hot and sunny.
(b) 7 + 8 = 15
(c) There is no air pollution in Karuppur
(d) Today is friday.
3. Let p and q be the propositions
p: I drive over 85 km per hour
q: I get a speeding ticket.
(a) I do not driver over 85 kmph
(b) I will get a speeding ticket if I drive over 85 kmph.
(c) Driving over 85 kmph is sufficient for getting a speeding ticket.
(d) Whenever I get a speeding ticket, I am driving over 85 kmph.
4. Obtain a truth table for each of the following propositional forms:
(a) (
)
¬ ∧
p q
(b) ¬ ∧
(
)
p q
(c) (
) (
)
¬ ∨ ¬
p
q
(d) (
)
p q r
∧ ∨
(e) (
(
))
p
p
p
∧ ¬
⇒
5. Determine whether each of the following implications is true or false.
(a) If 2 + 2 = 6, then 3 + 3 = 8
(b) If elephants can fly, then 2 + 2 = 6
(c) If 2 + 2 = 6, then elephants can fly.
6. For each of the following sentences state if the sentence means if the
“or” is an “inclusive or” (disjunction) or an “exclusive or” which of
these meanings of “or” do you think is intended
(a) Dinner for two includes two items from menu list I or three items
from menu list II.
(b) To take Applied Physics, you should have taken a course in
Mathematics or a course in physics.
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Theory of Automata, Formal Languages and Computation