Advertisements
Advertisements
Question
The negation of the statement “101 is not a multiple of 3” is ______.
Options
101 is a multiple of 3
101 is a multiple of 2
101 is an odd number
101 is an even number
Advertisements
Solution
The negation of the statement “101 is not a multiple of 3” is 101 is a multiple of 3.
Explanation:
Let p: 101 is not a multiple of 3.
~ p: 101 is a multiple of 3.
APPEARS IN
RELATED QUESTIONS
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive
Find out the sentence are statement and are not. Justify your answer.
Two non-empty sets have always a non-empty intersection.
Find out the sentence are statement and are not. Justify your answer.
The cat pussy is black.
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.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
x2 + 5 | x | + 6 = 0 has no real roots.
Write the negation of the statement:
It rained on July 4, 2005.
Write the negation of the statement:
Ravish is honest.
Write the negation of the statement:
The sun is cold.
Both the diagonals of a rectangle have the same length.
All policemen are thieves.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
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.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
To apply for a driving licence, you should have a ration card or a passport.
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 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.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
Write the negation of statement:
For every x ϵ N, x + 3 < 10
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.
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.
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 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.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
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?
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
A rectangle is a quadrilateral or a 5-sided polygon.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Rewrite the following statements in the form of conditional statements
The square of a prime number is not prime.
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 triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
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 even prime number other than 2.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
