Question

Asked Oct 15, 2019

For the given conditional statement write the contrapositive, converse, and inverse

Step 1

**(a)**

Consider the given statements: ‘If you can’t see my mirrors, then I can’t see you’

Now, write the required statements:

Contrapositive:

It is known that contrapositive of a statement, ‘If *P* then *Q*’ is ‘If not *Q* then not *P*’

Hence, the required contrapositive statement will be:

**‘If I can see you, then you can see my mirrors.’**

Converse:

It is known that converse of a statement, ‘If *P* then *Q*’ is ‘If *Q* then *P*’

Hence, the required converse statement will be:

**‘If I can’t see you, then you can’t see my mirrors.’**

** **

Inverse:

It is known that inverse of a statement, ‘If *P* then *Q*’ is ‘If not *P* then not *Q*’

Hence, the required inverse statement will be:

**‘If you can see my mirrors, then I can see you’**

Step 2

**(b)**

Consider the given statements: ‘If *n* is an even integer, then *n*2 is an even integer’

Now, write the required statements:

Contrapositive:

It is known that contrapositive of a statement, ‘If *P* then *Q*’ is ‘If not *Q* then not *P*’

Hence, the required contrapositive statement will be:

**‘If n2 is not an even integer, then n is not an even integer.’**

Converse:

It is known that converse of a statement, ‘If *P* then *Q*’ is ‘If *Q* then *P*’

Hence, the required converse statement will be:

**‘If n2 is an even intege...**

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