Advertisements
Advertisements
Question
Write the negation of the following statements:
p: All triangles are equilateral triangles.
Advertisements
Solution
We have
It is false that all triangles are equilateral triangles
or
~ p: Threre exists a triangle which is not an equilateral triangles.
or
~ p: Not all triangles are equilateral triangles
APPEARS IN
RELATED QUESTIONS
Show that the following statement is true by the method of contrapositive.
p: If x is an integer and x2 is even, then x is also even.
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.
There are 35 days in a month.
Find out the sentence are statement and are not. Justify your answer.
All real numbers are complex numbers.
Write the negation of the statement:
The earth is round.
Write the negation of the statement:
The sun is cold.
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:
r : There exists a number x such that 0 < x < 1.
Write the component statement of the compound statement and check whether the compound statement is true or false:
The sand heats up quickly in the sun and does not cool down fast at night.
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 rains only if it is cold.
Check the validity of the statement:
r : 60 is a multiple of 3 or 5.
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”
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”
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.
Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.
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
Where is your bag?
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
Translate the following statements into symbolic form
2, 3 and 6 are factors of 12
Write down the negation of following compound statements
35 is a prime number or a composite number
Rewrite the following statements in the form of conditional statements
You will fail, if you will not study.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.
Identify the Quantifiers in the following statements.
There exists a even prime number other than 2.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
The negation of the statement “72 is divisible by 2 and 3” is ______.
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?
