हिंदी

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 - Mathematics

Advertisements
Advertisements

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.

Advertisements

उत्तर

The given statement can be written in five different ways as follows.

(i) A natural number is odd implies that its square is odd.

(ii) A natural number is odd only if its square is odd.

(iii) For a natural number to be odd, it is necessary that its square is odd.

(iv) For the square of a natural number to be odd, it is sufficient that the number is odd.

(v) If the square of a natural number is not odd, then the natural number is not odd.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 14: Mathematical Reasoning - Exercise 14.4 [पृष्ठ ३३८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise 14.4 | Q 1 | पृष्ठ ३३८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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 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.


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.


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”.

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:

If it is hot outside, then you feel thirsty.


State the converse and contrapositive of  statement:

If you live in Delhi, then you have winter clothes.


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


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.


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 ______.


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×