Advertisements
Advertisements
Question
The negation of the statement “72 is divisible by 2 and 3” is ______.
Options
72 is not divisible by 2 or 72 is not divisible by 3
72 is not divisible by 2 and 72 is not divisible by 3
72 is divisible by 2 and 72 is not divisible by 3
72 is not divisible by 2 and 72 is divisible by 3
Advertisements
Solution
The negation of the statement “72 is divisible by 2 and 3” is 72 is not divisible by 2 and 72 is not divisible by 3.
Explanation:
Let p: 72 is divisible by 2 and 3
And q: 72 is divisible by 2
r: 72 is divisible by 3
∴ ~ q: 72 is not divisible by 2
~ r: 72 is not divisible by 3
So ~ (q ∧ r) : ~ q ∨ ~ r
⇒ 72 is not divisible by 2 or 72 is not divisible by 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
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.
p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
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.
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.
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.
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.
To entry a country, you need a passport or a voter registration card.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 4.
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.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
statement are true and false? In each case give a valid reason for saying so
t : \[\sqrt{11}\] is a rational number.
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
“2 is both an even number and a prime number”
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 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:
When you sing, my ears hurt.
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:
For all even integers x, x2 is also even.
Check the validity of the statements:
s: 60 is a multiple of 3 or 5.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
A triangle has three sides.
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 the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
6 is divisible by 2 and 3.
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: A natural number n is odd.
q: Natural number n is not divisible by 2.
Identify the Quantifiers in the following statements.
For all negative integers x, x 3 is also a negative integers.
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
