English

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

Question

State the converse and contrapositive of  statement:

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

Solution

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
  Is there an error in this question or solution?
Chapter 31: Mathematical reasoning - Exercise 31.5 [Page 21]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 31 Mathematical reasoning
Exercise 31.5 | Q 2.3 | Page 21

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”.

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.


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.


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.


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:

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".

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:

 Only if Max studies will he pass the test.


Determine the contrapositive of the statement:

If she works, she will earn money.


Determine the contrapositive of the statement:

 It never rains when it is cold.


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.


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 n is a natural number, then n is an integer.


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


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.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×