English

Write the Contrapositive and Converse of the Following Statements. X Is an Even Number Implies That X Is Divisible by 4

Advertisements
Advertisements

Question

Write the contrapositive and converse of the following statements.

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

Advertisements

Solution

The given statement can be written as follows.

If x is an even number, then x is divisible by 4.

The contrapositive is as follows.

If x is not divisible by 4, then x is not an even number.

The converse is as follows.

If x is divisible by 4, then x is an even number.

shaalaa.com
  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.

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 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.


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.


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:

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:

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”.

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:

 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".

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 Mohan is a poet, then he is poor.


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.


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.


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 = y and y = 3, then x = 3.


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


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


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 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×