Advertisements
Advertisements
Question
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
Solution
r: There exists a number x such that 0 < x < 1.
~r: For every real number x, either \[x \leq 0\] or \[x < 1\] .
APPEARS IN
RELATED QUESTIONS
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.
All triangles have three sides.
Give three examples of sentences which are not statements. Give reasons for the answers.
Write the negation of the statement:
The sun is cold.
All policemen are thieves.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
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.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
Write the negation of the statement:
q : For every real number x, either x > 1 or x < 1.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
To entry a country, you need a passport or a voter registration card.
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 component statement of the compound statement and check whether the compound statement is true or false:
All rational numbers are real and all real numbers are not complex.
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 England and 2 + 2 = 4.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
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
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.
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”
Write the negation of the following statements:
Suresh lives in Bhopal or he lives in Mumbai.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
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:
r: 100 is a multiple of 4 and 5.
Which of the following is a statement?
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
y + 9 = 7.
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
x and y are even integers.
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.
For all real numbers x with x > 3, x 2 is greater than 9.
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.
The negation of the statement “7 is greater than 8” is ______.
Which of the following statement is a conjunction?
