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.

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.

It the two lines are parallel, then they do not intersect in the same plane.


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”.

A quadrilateral is a parallelogram if its diagonals bisect each other.


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.


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.


State the converse and contrapositive of  statement:

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


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.


Determine the contrapositive of the statement:

 If Mohan is a poet, then he is poor.


Determine the contrapositive of the statement:

 It never rains when it is cold.


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:

 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.


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 and y are negative integers, then xy is positive.


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 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 x is zero, then x is neither positive nor negative.


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 ______.


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”.

q: There is a traffic jam whenever it rains.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×