मराठी

Statement Are True and False? in Each Case Give a Valid Reason for Saying Sot : √ 11 is a Rational Number.

Advertisements
Advertisements

प्रश्न

 statement are true and false? In each case give a valid reason for saying so

 t :  \[\sqrt{11}\]  is a rational number. 

 

 

Advertisements

उत्तर

 11 is a prime number and we know that the square root of any prime number is an irrational number. Therefore, 

\[\sqrt{11}\]  is an irrational number.

Thus, the given statement is false. 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Show that the statement

p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive


Give three examples of sentences which are not statements. Give reasons for the answers.


Write the negation of the statement:

 Ravish is honest.


Write the negation of the statement:

 p : For every positive real number x, the number (x − 1) is also positive.

 


Write the negation of the statement:

r : There exists a number x such that 0 < x < 1.

 

Write the component statement of the compound statement and check whether the compound statement is true or false:

 Square of an integer is positive or negative.i


Determine whether the compound statement are true or false:

 Delhi is in India and 2 + 2 = 4.
 


Write the negation of  statement:

 There exists x ϵ N, x + 3 = 10

 

Write of the statement in the form "if p, then q". 

 It rains only if it is cold.


Write of the statement in the form "if p, then q". 

 Whenever it rains it is cold.


Check the validity of the statement:

 p : 100 is a multiple of 4 and 5.


 statement are true and false? In each case give a valid reason for saying so

 p : Each radius of a circle is a chord of the circle.


 statement are true and false? In each case give a valid reason for saying so

r : Circle is a particular case of an ellipse.


Identify the component statements and the connective in the following compound statements.

It is raining or the sun is shining.


Rewrite the following statements in the form of conditional statements:

Ramesh will get dessert only if he eats his dinner.


Rewrite the following statements in the form of conditional statements:

When you sing, my ears hurt.


The negation of the statement “It is raining and weather is cold.” is ______.


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Translate the following statements into symbolic form

x and y are even integers.


Translate the following statements into symbolic form

2, 3 and 6 are factors of 12


Rewrite the following statements in the form of conditional statements

The unit digit of an integer is 0 or 5 if it is divisible by 5.


Rewrite the following statements in the form of conditional statements

The square of a prime number is not prime.


Rewrite the following statements in the form of conditional statements

2b = a + c, if a, b and c are in A.P.


Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.


Identify the Quantifiers in the following statements.

For all real numbers x and y, xy = yx.


Identify the Quantifiers in the following statements.

There exists a real number which is not a rational number.


Identify the Quantifiers in the following statements.

For every natural number x, x + 1 is also a natural number.


Check the validity of the following statement.
p: 125 is divisible by 5 and 7.


Check the validity of the following statement.
q: 131 is a multiple of 3 or 11


Which of the following is a statement?


Which of the following is not a statement>


The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.


The negation of the statement “7 is greater than 8” is ______.


The negation of the statement “72 is divisible by 2 and 3” is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×