26. Using the Switcheroo law p q
p q
→ ≡
∨
( )
7
transform the following
statement into a disjunction: “If 0 = 1, then I am the queen of Texas.”
27. Check whether the followings statements are equivalent or not.
(a) If it is Tuesday, this must be Mexico.
(b) That this is Mexico is a necessary condition
(c) Its being Tuesday is sufficient for this to be Mexico.
28. Verify whether commutative law holds good for the “conditional” i.e.,
p q
→ is the same as q
p
→ or not?
29. Prove the valid argument:
(
) (
)
p r
s t
p
t
∨ → ∧
∴
30. Prove the valid argument:
a
b c
b
a
→ ∧
¬
∴ ¬
(
)
31. Prove the valid argument:
p a
p b
p
a b
→
→
∴ ∧
32. Check the validity of the argument:
s r
p q
r
s
q r
p
q
→
∨ → ¬
¬ → ¬ →
∴
(
)
(
)
33. Prove and comment on the argument:
p
p
p
∧ ¬
∴
(
)
34. Show that the argument
p q
q
p
→
∴
is not valid.
296
Theory of Automata, Formal Languages and Computation