मराठी

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

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

Let p: n2 is an even integer.

q: n is also an even integer.

Also let ~ q is true i.e. n is not an even integer.

⇒ n2 is not an even integer   .....[∵ Square of an odd integer is odd]

⇒ ~ p is true.

Hence, ~ q is true ⇒ ~ p is true.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 14: Mathematical Reasoning - Exercise [पृष्ठ २६५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 14 Mathematical Reasoning
Exercise | Q 16 | पृष्ठ २६५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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”.

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


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”.

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.


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 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".

 p : If you watch television, then your mind is free and if your mind is free, then you watch television.


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:

If it snows, then they do not drive the car.


Determine the contrapositive of the statement:

 If Ravish skis, then it snowed.


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.


Check whether the statement are true or not: 

p : If x and y are odd integers, then x + 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 natural number n is divisible by 6, then n is divisible by 2 and 3.


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.


The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is ______.


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 ______.


Write the statement in the form “if p, then q”.

p: It is necessary to have a password to log on to the server.


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×