State
the converse and contrapositive of each of the following statements:
(i) p:
A positive integer is prime only if it has no divisors other than 1
and itself.
(ii) q:
I go to a beach whenever it is a sunny day.
(iii) r:
If it is hot outside, then you feel thirsty.
State the converse and contrapositive of each of the following statements:
(i) p: A positive integer is prime only if it has no divisors other than 1 and itself.
(ii) q: I go to a beach whenever it is a sunny day.
(iii) r: If it is hot outside, then you feel thirsty.
(i) Statement
p
can be written as follows.
If
a positive integer is prime, then it has no divisors other than 1 and
itself.
The
converse of the statement is as follows.
If
a positive integer has no divisors other than 1 and itself, then it
is prime.
The
contrapositive of the statement is as follows.
If
positive integer has divisors other than 1 and itself, then it is not
prime.
(ii) The
given statement can be written as follows.
If
it is a sunny day, then I go to a beach.
The
converse of the statement is as follows.
If
I go to a beach, then it is a sunny day.
The
contrapositive of the statement is as follows.
If
I do not go to a beach, then it is not a sunny day.
(iii) The
converse of statement r
is as follows.
If
you feel thirsty, then it is hot outside.
The
contrapositive of statement r
is as follows.
If
you do not feel thirsty, then it is not hot outside.
(i) Statement p can be written as follows.
If a positive integer is prime, then it has no divisors other than 1 and itself.
The converse of the statement is as follows.
If a positive integer has no divisors other than 1 and itself, then it is prime.
The contrapositive of the statement is as follows.
If positive integer has divisors other than 1 and itself, then it is not prime.
(ii) The given statement can be written as follows.
If it is a sunny day, then I go to a beach.
The converse of the statement is as follows.
If I go to a beach, then it is a sunny day.
The contrapositive of the statement is as follows.
If I do not go to a beach, then it is not a sunny day.
(iii) The converse of statement r is as follows.
If you feel thirsty, then it is hot outside.
The contrapositive of statement r is as follows.
If you do not feel thirsty, then it is not hot outside.
