English

Write the truth value of the following statements.(i) 9 is an even integer or 9 + 1 is even.(ii) 2 + 4 = 6 or 2 + 4 = 7(iii) Delhi is the capital of India and Islamabad is the capital

Advertisements
Advertisements

Question

Write the truth value of the following statements.
(i) 9 is an even integer or 9 + 1 is even.
(ii) 2 + 4 = 6 or 2 + 4 = 7
(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.
(iv) Every rectangle is a square and every square is a rectangle
(v) The sun is a star or sun is a planet.

Sum
Advertisements

Solution

In view of (D1), (D2), (D3) and (D4),

We observe that only statement (iv) has truth value F as the first component statement namely “every rectangle is a square” is false.

Further, in statements (i), (ii) and (v) atleast one component statement is true.

Therefore, these statements have truth value T.

Also, truth value of statement (iii) is T as both the component statements are true

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Solved Examples [Page 256]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 11
Chapter 14 Mathematical Reasoning
Solved Examples | Q 4 | Page 256

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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

Two non-empty sets have always a non-empty intersection.


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.

Every rhombus is a square.


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

 x2 + 5 | x | + 6 = 0 has no real roots.


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

 This sentence is a statement.


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

 Go !


 Both the diagonals of a rectangle have the same length.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

A lady gives birth to a baby boy or a baby girl.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

 To apply for a driving licence, you should have a ration card or a passport.

 

Determine whether the compound statement are true or false:

 Delhi is in England and 2 + 2 = 4.
 


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

 It rains only if it is cold.


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

q : The centre of a circle bisects each 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. 

 

 


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.


Which of the following statements are compound statements 

“2 is both an even number and a prime number”


Which of the following statements are compound statements 

“Ram and Rahim are friends”


Translate the following statements in symbolic form

2 and 3 are prime numbers 


Write negation of the statement
“Everyone who lives in India is an Indian”


Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.


Check the validity of the statements:
s: 60 is a multiple of 3 or 5.


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


Which of the following sentences are statements? Justify

15 + 8 > 23


Find the component statements of the following compound statements.

Plants use sunlight, water and carbon dioxide for photosynthesis.


Write the component statements of the following compound statements and check whether the compound statement is true or false.

57 is divisible by 2 or 3.


Write the component statements of the following compound statements and check whether the compound statement is true or false.

2 is an even number and a prime number.


Translate the following statements into symbolic form

Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0


Write down the negation of following compound statements

All real numbers are rationals or irrationals.


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 triangle which is not equilateral.


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 triangle which is not an isosceles triangle.


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


The negation of the statement “The product of 3 and 4 is 9” is ______.


Which of the following statement is a conjunction?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×