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**Exercise 14.4**

**1. Rewrite the following statements with “if-then” in five different ways conveying the same meaning.**

**If a natural number is off then its square is also odd.**

**Ans. (i) **A natural number is odd implies that its square is odd.

**(ii) **A natural is odd only if its square is odd.

**(iii) **For a natural number to be odd it is necessary that its square is odd.

**(iv) **For the square of a natural number to be odd it is sufficient that the number is odd.

**(v) **If the square of a natural number is not odd then the natural number is not odd.

**2. Write the contrapositive and converse of the following statements:**

**(i) If **** is a prime number, then **** is odd.**

**(ii) If the two lines are parallel, then they do not intersect in the same plane.**

**(iii) Something is cold implies that is 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 4.**

**Ans. (i) **The contrapositive of given statement is: If is not odd then is not a prime number.

The converse of the given statement is: If is an odd number then is a prime number.

**(ii) **The contrapositive of given statement is: If two lines intersect in the same plane then they are not parallel.

The converse of the given statement is: If the two lines do not intersect in the same plane they are parallel.

**(iii) **The contrapositive of given statement is: If something does not have low temperature then it is not cold.

The converse of the given statement is: If something has low temperature then it is cold.

**(iv) **The contrapositive of given statement is: If you know to reason deductively then you can comprehend geometry.

The converse of the given statement is: If you do not know to reason deductively then you cannot comprehend geometry.

**(v) **The contrapositive of given statement is: If is not divisible by 4 then is not an even number.

The converse of the given statement is: If is divisible by 4 then is an even number.

**3. Write each of the following statements in the form “if-then”:**

**(i) You get a job implies that your credentials are good.**

**(ii) The Banana tree will bloom if it stays warm for a month.**

**(iii) A quadrilateral is a parallelogram, if its diagonals bisect each other.**

**(iv) To get an A ^{+} in the class then you do all the exercises of the book.**

**Ans. (i) **If you get a job then you credentials are good.

**(ii) **If it says warm for a month then the banana trees will bloom.

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

**(iv) **If you get in the class then you do all the exercises in the book.

**4. Give statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other:**

**(a) If you live in Delhi, then you have winter clothes.**

**(i) If you do not have winter clothes, then you do not live in Delhi.**

**(ii) If you have winter clothes, then you live in Delhi.**

**(b) If a quadrilateral is a parallelogram then its diagonals bisect each other.**

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

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

**Ans. (a)** **(i)** Contrapositive **(ii)** Converse

**(b)** **(i)** Contrapositive **(ii)** Converse