** ****Q.1: Rewrite the statements with ‘if & then’ in 5 different ways but the sentence should convey the meaning as before.**

**A natural number is odd implies that its square is odd. **

** **

**Sol:**

**(a).** A If the square of the natural number is said to be odd then the number is odd too.

**(b).** If the square of a number is not even then the natural number which is squared is also odd.

**(c).** It is mandatory that the square of a number to be not even (odd) in order to have that natural number as odd.

**(d).** If the natural number is not odd then the square of that number is also not odd that is even.

**(e).** In order to have the square of a number (natural number) which is odd, it is sufficient that the number (natural number) is also odd.

**Q.2: Rewrite the following sentences as the converse/contrapositive of the followings:**

**(a). A quadrilateral is said to be parallelogram if the diagonals bisect each other.**

**(b). y is an odd number that is y is divisible by 3**

**(c). If 2 lines do not intersect in the same plane, then they are said to be parallel.**

**(d). If something is having a low temperature then it implies that is cold **

**(e). If you are not able to deduct the reason, then you will not be able to comprehend geometry.**

** **

** Sol:**

**(a)** **Contrapositive – ** If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

**Converse** **–** If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

**(b) Contrapositive –** If y is not divisible by 3 then it is not an odd number.

**Converse –** If y is divisible by 3 , then it is an odd number.

**(c) Contrapositive –** If 2 lines intersect in the same plane, then they are not parallel.

**Converse –** If 2 lines do not intersect in the same plane, then they are parallel.

**(d) Contrapositive –** If something does not have low temperature, then it implies that it is not cold

**Converse –** If something is having at a low temperature, then it implies that it is cold.

**(e) Contrapositive –** If you know how to reason deductively, then you can comprehend geometry.

**Converse –** If you do not know how to reason deductively, then you cannot comprehend geometry.

**Q.3: Rewrite the following sentences with “if- then”:**

**(a). You have visited Qutub Minar implies that you live in Delhi**

**(b). You will pass the exam if you study hard.**

**(c). In order to get A+ in the class test, you have to do all the problems of that chapter.**

**(d). Parallel lines do not intersect each other in the same plane **

** **

**Sol:**

**(a) If you have visited Qutub Minar then you live in Delhi. **

**(b) If you study hard then you will pass the exam**

**(c) If you want to get A+ in the class test then you have to do all the problems of the book.**

**(d) If two lines are parallel then they do not intersect each other in the same plane.**

**Q.4: Identify the contrapositive/converse from the following sentences:**

**(i) **If you live in **Agra**, then you have visited **Taj Mahal**

**(a) **If you have not visited** Taj Mahal **then you do not live in **Agra.**

**(b) ** If you have visited **Taj Mahal** then you live in **Agra.**

**(ii) **If the diagonals of the quadrilateral bisect each other then that **quadrilateral is a parallelogram.**

**(a) **A **quadrilateral is not said to be a parallelogram** if the diagonals of a quadrilateral do not bisect each other.

**(b) **A **quadrilateral is said to be a parallelogram** if the diagonals of a quadrilateral bisect each other.

** **

**Sol:**

**(i).**

**(a)** **Statement I is the contrapositive** of the above mentioned statement

**(b)** **Statement II is the converse** of the above mentioned statement

**(ii).**

**(a)** **Statement I is the contrapositive** of the above mentioned statement

**(b)** **Statement II is the converse** of the above mentioned statement

** **