Advertisements
Advertisements
प्रश्न
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is an irrational number.
Advertisements
उत्तर
The number x is not a rational number.
The number x is an irrational number.
The statements in this pair are not the negation of each other because both statements are the same. Both the statements convey that x is an irrational number.
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.
x2 + 5 | x | + 6 = 0 has no real roots.
Find out the sentence are statement and are not. Justify your answer.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
The product of (−1) and 8 is 8.
Give three examples of sentences which are not statements. Give reasons for the answers.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
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:
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 = 5.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
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 is necessary to have a passport to log on to the server.
Write of the statement in the form "if p, then q".
It never rains when it is cold.
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
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
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.
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Write the negation of the following statements:
q: 9 is a multiple of 4.
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Which of the following sentences are statements? Justify
Where is your bag?
Find the component statements of the following compound statements.
Number 7 is prime and odd.
Find the component statements of the following compound statements.
Chennai is in India and is the capital of Tamil Nadu.
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
Either x or x + 1 is an odd integer.
Translate the following statements into symbolic form
Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
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.
q: 131 is a multiple of 3 or 11
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 statement is a conjunction?
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
