English

The contrapositive of the statement “If p, then q”, is ______.

Advertisements
Advertisements

Question

The contrapositive of the statement “If p, then q”, is ______.

Options

  • If q, then p

  • If p, then ~ q

  • If ~ q, then ~ p

  • If ~ p, then ~ q

MCQ
Fill in the Blanks
Advertisements

Solution

The contrapositive of the statement “If p, then q”, is if ~ q, then ~ p.

Explanation:

Here the statement is “If p, then q”

i.e. p → q

Contrapositive of the statement p → q is (~ q) → (~ p)

i.e., If ~ q, then ~ p.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Exercise [Page 268]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 30 | Page 268

Video TutorialsVIEW ALL [1]

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.

If x is a prime number, then x is odd


Write the contrapositive and converse of the following statements.

Something is cold implies that it has low temperature.


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”.

To get A+ in the class, it is necessary that you do the exercises of the book.


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

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

 


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

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


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.


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 a quadrilateral is a parallelogram, then its diagonals bisect each other.

 

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".

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


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:

If x is less than zero, then x is not positive.


Determine the contrapositive of the statement:

 If he has courage he will 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: 

 q : If xy 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 natural number n is divisible by 6, then n is divisible by 2 and 3.


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


Write down the converse of following statements:

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


Write down the converse of following statements:

If two triangles are similar, then the ratio of their corresponding sides are equal.


The converse of the statement “If x > y, then x + a > y + a” is ______.


The converse of the statement “If sun is not shining, then sky is filled with clouds” 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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×