मराठी

Determine Whether the Argument Used to Check the Validity of the Following Statement is Correct: P : "If X2 is Irrational, Then X is Rational" - Mathematics

Advertisements
Advertisements

प्रश्न

Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.

उत्तर

The argument used to check the validity of the given statement is false because it is given in the argument that x= π is irrational and therefore x = π is irrational; however, according to the statement, is rational.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 31: Mathematical reasoning - Exercise 31.6 [पृष्ठ २९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 31 Mathematical reasoning
Exercise 31.6 | Q 8 | पृष्ठ २९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

By giving a counter example, show that the following statements are not true.

p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.


Find out the sentence are statement and are not. Justify your answer.

 Every set is a finite set.


Find out the sentence are statement and are not. Justify your answer.

 Are all circles round?


Find out the sentence are statement and are not. Justify your answer.

 The real number x is less than 2.


Find out the sentence are statement and are not. Justify your answer.

 Mathematics is difficult.


Find out the sentence are statement and are not. Justify your answer.

The product of (−1) and 8 is 8.

 

 Some even integers are prime.


There is a complex number which is not a real number.


All policemen are thieves.

 

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

The sand heats up quickly in the sun and does not cool down fast at night.

 

Determine whether the compound statement are true or false:

 Delhi is in India and 2 + 2 = 4.
 


Write the negation of  statement:

For every x ϵ Nx + 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". 

 It never rains when it is cold.

 

 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

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

 

 


Which of the following statements are compound statements 

“Ram and Rahim are friends”


Write the negation of the following statements:
r: A triangle has four sides.


Write the negation of the following statements:
x + y = y + x and 29 is a prime number.


Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4


Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”


Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.


Which of the following sentences are statements? Justify

0 is a complex number.


Which of the following sentences are statements? Justify

Every set is an infinite set.


Which of the following sentences are statements? Justify

Sum of opposite angles of a cyclic quadrilateral is 180°.


Which of the following sentences are statements? Justify

sin2x + cos2x = 0


Find the component statements of the following compound statements.

Two lines in a plane either intersect at one point or they are parallel.


Translate the following statements into symbolic form

Rahul passed in Hindi and English.


Translate the following statements into symbolic form

A number is either divisible by 2 or 3.


Write down the negation of following compound statements

x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.


Rewrite the following statements in the form of conditional statements

You will get a sweet dish after the dinner.


Identify the Quantifiers in the following statements.

There exists a even prime number other than 2.


Identify the Quantifiers in the following statements.

There exists a real number x such that x2 + 1 = 0.


The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.


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


The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.


Which of the following is the conditional p → q?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×