Advertisements
Advertisements
Question
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Advertisements
Solution
The quantifier is “for all” and the negation is
“There exists an even integer x such that x2 is not even”
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.
This sentence is a statement.
Some even integers are prime.
I will not go to school.
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 an irrational number.
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.
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
Write the negation of statement:
For every x ϵ N, x + 3 < 10
Negate statement:
All the students completed their homework.
Write of the statement in the form "if p, then q".
It is necessary to be rich in order to be happy.
Write of the statement in the form "if p, then q".
It rains only if it is cold.
Which of the following statements are compound statements
“9 is neither an even number nor a prime number”
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Write the negation of the following statements:
p: All triangles are equilateral triangles.
Write the negation of the following statements:
q: 9 is a multiple of 4.
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:
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
Sum of opposite angles of a cyclic quadrilateral is 180°.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.
Find the component statements of the following compound statements.
A rectangle is a quadrilateral or a 5-sided polygon.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Identify the Quantifiers in the following statements.
There exists a triangle which is not equilateral.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
Identify the Quantifiers in the following statements.
For all negative integers x, x 3 is also a negative integers.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
The negation of the statement “A circle is an ellipse” is ______.
Which of the following is the conditional p → q?
The negation of the statement “The product of 3 and 4 is 9” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
