###### Advertisements

###### Advertisements

Write each of the following statement in the form “if-then”.

A quadrilateral is a parallelogram if its diagonals bisect each other.

###### Advertisements

#### Solution

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

#### APPEARS IN

#### RELATED QUESTIONS

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

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

Write the contrapositive and converse of the following statements.

It the two lines are parallel, then they do not intersect in the same plane.

Write the contrapositive and converse of the following statements.

You cannot comprehend geometry if you do not know how to reason deductively.

Write the contrapositive and converse of the following statements.

*x* is an even number implies that *x* is divisible by 4

Write each of the following statement in the form “if-then”.

The Banana trees will bloom if it stays warm for a month.

Given 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 it is a parallelogram.

State the converse and contrapositive of each of the following statements:

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

**Write the statement in the form “if p, then q”.**

r: You can access the website only if you pay a subscription fee.

Re write each of the following statements in the form “*p* if and only if *q*”.

*p*: If you watch television, then your mind is free and if your mind is free, then you watch television.

Re write each of the following statements in the form “*p* if and only if *q*”.

*r*: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

State the converse and contrapositive of statement:

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

State the converse and contrapositive of statement:

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

Rewrite of the statement in the form "*p* if and only if *q*".

*p* : If you watch television, then your mind is free and if your mind is free, then you watch television.

Rewrite of the statement in the form "*p* if and only if *q*".

*q* : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Rewrite of the statement in the form "*p* if and only if *q*".

*r* : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Rewrite of the statement in the form "*p* if and only if *q*".

*s* : If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.

Determine the contrapositive of the statement:

If Mohan is a poet, then he is poor.

Determine the contrapositive of the statement:

If she works, she will earn money.

Determine the contrapositive of the statement:

If it snows, then they do not drive the car.

Determine the contrapositive of the statement:

It is necessary to be strong in order to be a sailor.

Determine the contrapositive of the statement:

Only if he does not tire will he win.

Determine the contrapositive of the statement:

If *x* is an integer and *x*^{2} is odd, then *x* is odd.

Check whether the statement are true or not:

*q* : If *x*, *y* are integers such that *xy* is even, then at least one of *x* and *y* is an even integer.

Which of the following is the converse of the statement?

“If Billu secure good marks, then he will get a bicycle.”

Write down the contrapositive of the following statements:

If n is a natural number, then n is an integer.

Write down the contrapositive of the following statements:

If x and y are negative integers, then xy is positive.

Write down the contrapositive of the following statements:

If it snows, then the weather will be cold.

Write down the converse of following statements:

If you go to Agra, then you must visit Taj Mahal.

Write down the converse of following statements:

If the sum of squares of two sides of a triangle is equal to the square of third side of a triangle, then the triangle is right-angled.

Write down the converse of following statements:

If x is zero, then x is neither positive nor negative.

The statement “If x^{2} is not even, then x is not even” is converse of the statement ______.