Advertisements
Advertisements
Question
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
Advertisements
Solution
p: For every positive real number x, the number (x − 1) is also positive.
~p: At least for one positive real number x, the number
APPEARS IN
RELATED QUESTIONS
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.
Go !
Write the negation of the statement:
The sun is cold.
There is a complex number which is not a real 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.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
Find the component statement of the compound statement:
All rational numbers are real and all real numbers are complex.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
Students can take Hindi or Sanskrit as their third language.
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 =5.
Write of the statement in the form "if p, then q".
You can access the website only if you pay a subscription fee.
Write of the statement in the form "if p, then q".
There is traffic jam whenever it rains.
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.
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.
Write the negation of the following statements:
x + y = y + x and 29 is a prime number.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
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
sin2x + cos2x = 0
Find the component statements of the following compound statements.
Number 7 is prime and odd.
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.
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
Write down the negation of following compound statements
35 is a prime number or a composite number
Write down the negation of following compound statements
|x| is equal to either x or – x.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
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.
For all real numbers x and y, xy = yx.
Identify the Quantifiers in the following statements.
There exists a real number which is not a rational number.
Identify the Quantifiers in the following statements.
For every natural number x, x + 1 is also a natural number.
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.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
