English

State the Converse and Contrapositive of Each of the Following Statements: Q: I Go to a Beach Whenever It is a Sunny Day. - Mathematics

Advertisements
Advertisements

Question

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

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

Advertisements

Solution

The given statement can be written as follows.

If it is a sunny day, then I go to a beach.

The converse of the statement is as follows.

If I go to a beach, then it is a sunny day.

The contrapositive of the statement is as follows.

If I do not go to a beach, then it is not a sunny day.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Miscellaneous Exercise [Page 345]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Miscellaneous Exercise | Q 2.2 | Page 345

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.

Something is cold implies that it has low temperature.


Write the contrapositive and converse of the following statements.

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


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

You get a job implies that your credentials are good.


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

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


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”.

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


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.


Given below are two statements

p: 25 is a multiple of 5.

q: 25 is a multiple of 8.

Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.


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.


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:

 Only if Max studies will he pass the test.


Determine the contrapositive of the statement:

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


Determine the contrapositive of the statement:

 If Ravish skis, then it snowed.


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.


Check whether the statement are true or not: 

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


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 all three sides of a triangle are equal, then the triangle is equilateral.


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 x is a real number such that 0 < x < 1, then x2 < 1.


Write down the converse of following statements:

If a rectangle ‘R’ is a square, then R is a rhombus.


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 : y = 3 : 2, then 2x = 3y.


Write down the converse of following statements:

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


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


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 ______.


The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is ______.


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

p: It is necessary to have a password to log on to the server.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×