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Determine the Contrapositive of the Statement: If It Snows, Then They Do Not Drive the Car. - Mathematics

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प्रश्न

Determine the contrapositive of the statement:

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

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उत्तर

 If they do not drive the car, then there is no snow.

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पाठ 31: Mathematical reasoning - Exercise 31.5 [पृष्ठ २१]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 31 Mathematical reasoning
Exercise 31.5 | Q 4.04 | पृष्ठ २१

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संबंधित प्रश्‍न

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 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.


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

r: If it is hot outside, then you feel thirsty.


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:

If it is hot outside, then you feel thirsty.


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.


State the converse and contrapositive of  statement:

If you live in Delhi, then you have winter clothes.


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 Ravish skis, then it snowed.


Determine the contrapositive of the statement:

 If he has courage he will win.


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 x2 is odd, then x is odd.

 

Check whether the statement are true or not: 

p : If x and y are odd integers, then x + y is an even integer.


Check whether the statement are true or not: 

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


Show that the following statement is true.
p: For any real numbers x, y if x = y, then 2x + a = 2y + a when a ∈ Z.


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 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 today is Monday, then tomorrow is Tuesday.


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 S is a cyclic quadrilateral, then the opposite angles of S are supplementary


Using contrapositive method prove that if n2 is an even integer, then n is also an even integers.


The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.


The statement “If x2 is not even, then x is not even” is converse of the statement ______.


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

q: There is a traffic jam whenever it rains.


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