(b) p : Naveena takes Maths
q : Nirmala takes physics
r : Anju takes English
Then the given statement is written as
(
)
p q
r
∧ ⇒
(c) p : Ticket is available
q : I will travel by this train.
p q
⇒
is the given statement in symbolic form.
(d) p : There is a fault with Raju.
q : There is a fault with Mohan.
p q
∨
is the given statement is symbolic form.
Ì Exam ple 8.1.3: Given
p : Triangle PQR is isosceles
q : Triangle PQR is equilateral
r : Triangle PQR is equiangular.
Translate each of the following into a statement in English.
(a) q
p
⇔
(b) ¬ ⇔ ¬
p
q
(c) q
r
⇔
(d) p q
∧ 7
(e) r
p
⇒ .
Solu tion
(a) q
p
⇔
Triangle PQR is equilateral if and only if it is isoscles
(b) ¬ ⇔ ¬
p
q
Triangle PQR is not isosciles if and only if it is not equilateral.
(c) q
r
⇔
Triangle PQR is equilateral if and only if it is equiangular
(d) p
q
∧ ¬
Triangle PQR is isosceles and it is not equilateral.
(e) r
p
⇒
If Triangle PQR is equiangular then it is isosceles.
Prop o si tions and Pred i cates
251