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प्रश्न
Negate of the statement :
There exists a number which is equal to its square.
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उत्तर
Negation of the given statement:
There exists a number which is not equal to its square.
APPEARS IN
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
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.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
All policemen are thieves.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
There exist real numbers a and b for which a + b = b + a.
Write the component statement of the compound statement and check whether the compound statement is true or false:
To enter into a public library children need an identity card from the school or a letter from the school authorities.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 = 4.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =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.
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.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Write negation of the statement
“Everyone who lives in India is an Indian”
Write the negation of the following statements:
q: 9 is a multiple of 4.
Write the negation of the following statements:
r: A triangle has four sides.
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.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
y + 9 = 7.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
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.
All living things have two eyes and two legs.
Translate the following statements into symbolic form
x and y are even integers.
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.
Write down the negation of following compound statements
35 is a prime number or a composite number
Identify the Quantifiers in the following statements.
For all real numbers x with x > 3, x 2 is greater than 9.
Identify the Quantifiers in the following statements.
For all negative integers x, x 3 is also a negative integers.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
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?
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
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 “Rajesh or Rajni lived in Bangalore” is ______.
The negation of the statement “101 is not a multiple of 3” is ______.
