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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 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
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(i) Statement can be written as follows
If a positive integer is prime, then it has no divisors other than and itself.
The converse of the statement is as follows
If a positive integer has no divisors other than and itself then it is prime.
The contrapositive of the statement is as follows
If positive integer has divisors other than and itself 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 is as follows
If you feel thirsty then it is hot outside.
The contrapositive of statement is as follows
If you do not feel thirsty then it is not hot outside.
If a positive integer is prime, then it has no divisors other than and itself.
The converse of the statement is as follows
If a positive integer has no divisors other than and itself then it is prime.
The contrapositive of the statement is as follows
If positive integer has divisors other than and itself 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 is as follows
If you feel thirsty then it is hot outside.
The contrapositive of statement is as follows
If you do not feel thirsty then it is not hot outside.
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Question 2
Write the contrapositive and converse of the following statements(i) If is a prime number then is odd
(ii) It the two lines are parallel then they do not intersect in the same plane
(iii) Something is cold implies that it has low temperature
(iv) You cannot comprehend geometry if you do not know how to reason deductively
(v) is an even number implies that is divisible by
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| Question Text | 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 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 |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
