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Translate the following statements into symbolic form Rahul passed in Hindi and English. - Mathematics

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प्रश्न

Translate the following statements into symbolic form

Rahul passed in Hindi and English.

योग
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उत्तर

p: Rahul passed in Hindi.

q: Rahul passed in English

p ∧ q: Rahul passed in Hindi and English.

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अध्याय 14: Mathematical Reasoning - Exercise [पृष्ठ २६२]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise | Q 5.(i) | पृष्ठ २६२

वीडियो 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.


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

q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.


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.

 The real number x is less than 2.


Write the negation of the statement:

 Ravish is honest.


Are the pair of statement are negation of each other:

 The number x is not a rational number.
The number is an irrational number.


Write the negation of the statement:

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

 

Find the component statement of the compound statement:

 25 is a multiple of 5 and 8.

 

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.


Write the negation of  statement:

 There exists x ϵ Nx + 3 = 10

 

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

There is traffic jam whenever it rains.


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.


Check the validity of the statement:

q : 125 is a multiple of 5 and 7.


Check the validity of the statement:

 r : 60 is a multiple of 3 or 5.

 

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

 s : If x and y are integers such that x > y, then − x < − y.


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 

“9 is neither an even number nor a prime number”


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

It is raining or the sun is shining.


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.


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


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


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 equal to its square.


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.


Find the component statements of the following compound statements.

A rectangle is a quadrilateral or a 5-sided polygon.


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

All living things have two eyes and two legs.


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

Students can take Hindi or English as an optional paper.


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 fail, if you will not study.


Identify the Quantifiers in the following statements.

There exists a triangle which is not equilateral.


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


The negation of the statement “Plants take in CO2 and give out O2 ” is ______.


The negation of the statement “101 is not a multiple of 3” is ______.


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