35. Check whether the following argument is valid. If it is, then give a
proof, if it is not, then give a counterexample.
“Heat dissipation accompanies every irreversible chemical reaction.
Therefore, if a chemical reaction is reversible, it dissipates no heat”.
36. Check whether the following is valid.
If it is, then give a proof; it it is not, then give a counterexample.
“It the moon is made of red chease, then elephants can fly and circles are
round. The moon is indeed made of red cheese. Therefore elephants can
fly”.
37. Prove the valid argument
(
) (
)
p q
r s
p q
r s
∧ → ∨
∧
∴ ∨
38. Check the validity of the following arguments:
(a) ¬ ∨
∧ → ∨
∴ ¬ ∧
(
)
(
) (
)
(
)
r s
p q
r s
p q
(b) p q
p r
r
∧
→
∴
(c) p
q r
p
r
q
→ ∨
¬
(
)
39. Let P(x) denote “x spends more than six hours every weak is class”,
where the universe of discourse for x is the set of students. Express each
of the following quantifications in English.
(a) ℑ x P x
( )
(b) ∨ x P x
( )
(c) ℑ ¬
x
P x
( )
(d) ∨ ¬
x
P x
( )
40. Given P (x): x can speak Hindi
Q (x): x knows computer language “Small Talk” express each of the
following sentences in terms of P(x), Q(x), quantifiers and logical
connectives. Universe of discourse is the set of all students at your
school.
(a) There is a student at your school who can speak Hindi and who
knows small talk.
(b) There is a student at your school who can speak Hindi but who
does not know small talk.
41. Use quantifiers to express the associative law for multiplication of real
numbers.
Prop o si tions and Pred i cates
297