Since both statements are false, the biconditional p q
⇔ is true.
(ii) Consider the statement:
“I teach mathematics if and only if I am paid a large amount of
money”.
Some of the equivalent ways of phrasing this sentence are:
“My teaching Mathematics is necessary and sufficient for me to be
paid a large amount of money”.
“For me to teach Mathematics it is necessary and sufficient that I be
paid a large sum of money”.
Ì Exam ple 8.1.1: Express the following statements in symbolic form,
with
p : Jalaney is good.
q : Padmaja is good.
(a) Jalaney is good and Padmaja is not good.
(b) Jalaney and Padmaja are both good.
(c) Neither Jalaney nor Padmaja are good.
(d) It is not true that Jalaney and Padmaja are both good.
Solu tion
(a) p
q
∧ ¬
(b) p q
∧
(c) ¬ ∧ ¬
p
q
(d) ¬ ∧
(
)
p q
Ì Exam ple 8.1.2: Express the following statements in symbolic form.
(a) Jack and Jill went behind the hill
(b) If either Naveena takes Maths or Nirmala takes Physics, then Anju
will take English.
(c) If there is a ticket available, I will travel by this train
(d) There is either a fault with Raju or Mohan.
Solu tion
(a) p : Jack went behind the hill
q : Jill went behind the hill.
Then we have the given statement in symbolic form as
p q
∧
250
Theory of Automata, Formal Languages and Computation