Answer

Verified

446.4k+ views

**Hint:**We will first write the definitions of converse and contrapositive and then, write the given statements in the form required. After then apply all the definitions to given statements. Use the conditional statements topic.

**Complete step-by-step answer:**

Let us first write the definitions of converse and contrapositive:-

Converse:- If we have a statement with format “If p, then q” where p and q are the lines explaining the event, then its converse will be totally opposite that is “If q, then p”.

Contrapositive:- If we have a statement with format “If p, then q” where p and q are the lines explaining the event, then its contrapositive will be “If not q, then not p”. We can also represent this as “If $ \sim q$ then, $ \sim p$.

Let us now go to the first statement:

a : A positive integer is prime only if it has no divisors other than 1 and itself.

We can rewrite it as:

a: If a positive integer is prime, then it has no divisors other than 1 and itself.

Comparing it with “If p, then q”:

Here, p = a positive integer is prime and q = it has no divisors other than 1 and itself.

The converse of the statement will be “If q, then p” that is as follows:

If a positive integer has no divisors other than 1 and itself then it is prime.

The contrapositive of the statement will be “If $ \sim q$ then, $ \sim p$” that is as follows:

If a positive integer has divisors other than 1 and itself it is not prime.

Let us now go to the second statement:

b : I go to a beach whenever it is a sunny day.

We can rewrite it as:

b: If it is a sunny day then I go to a beach.

Comparing it with “If p, then q”:

Here, p = a it is a sunny day and q = I go to a beach.

The converse of the statement will be “If q, then p” that is as follows:

If I go to a beach then it is a sunny day.

The contrapositive of the statement will be “If $ \sim q$ then, $ \sim p$” that is as follows:

If I do not go to a beach then it is not a sunny day.

Let us now go to the third statement:

c : If it is hot outside then you feel thirsty.

Comparing it with “If p, then q”:

Here, p = it is hot outside and q = you feel thirsty.

The converse of the statement will be “If q, then p” that is as follows:

If you feel thirsty then it is hot outside.

The contrapositive of the statement will be “If $ \sim q$ then, $ \sim p$” that is as follows:

If you do not feel thirsty then it is not hot outside.

**Note:**We must not start with the given sentence always. We need to rewrite in the form “If p, then q”, because otherwise we may misplace p and q with each other.

Do not always tend to change the sentence because as in the statement c, we already had our desired form. SO, we didn’t change it.

Fact:- Contrapositive is always true if the original statement was true but converse need not be true. So, do not mistake all of these statements to be equivalent.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE