मराठी

State the Converse and Contrapositive of Statement: a Positive Integer is Prime Only If It Has No Divisors Other than 1 and Itself. - Mathematics

Advertisements
Advertisements

प्रश्न

State the converse and contrapositive of  statement:

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

Advertisements

उत्तर

Converse of the given statement:
If a positive integer has no divisors other than 1 and itself, then it is prime.
Contrapositive of the given statement:
If a positive integer has some divisors other than 1 and itself, then it is not prime.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 31: Mathematical reasoning - Exercise 31.5 [पृष्ठ २१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 31 Mathematical reasoning
Exercise 31.5 | Q 2.3 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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

You get a job implies that your credentials are good.


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”.

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


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.


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 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 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.


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


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


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×