Advertisements
Advertisements
Question
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
Advertisements
Solution
Given that p: 125 is divisible by 5 and 7.
Let q: 125 is divisible by 5.
And r: 125 is divisible by 7.
Here q is true and r is false.
⇒ q ∧ r is false.
Hence, p is not valid.
APPEARS IN
RELATED QUESTIONS
Show that the statement “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example.
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.
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.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
Every rhombus is a square.
Give three examples of sentences which are not statements. Give reasons for the answers.
Write the negation of the statement:
The sun is cold.
I will not go to school.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
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".
The game is cancelled only if it is raining.
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.
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.
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 the negation of the following statements:
q: 9 is a multiple of 4.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
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 sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Find the component statements of the following compound statements.
Chandigarh is the capital of Haryana and U.P.
Find the component statements of the following compound statements.
Two lines in a plane either intersect at one point or they are parallel.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Write down the negation of following compound statements
All rational numbers are real and complex.
Rewrite the following statements in the form of conditional statements
You will fail, if you will not study.
Rewrite the following statements in the form of conditional statements
2b = a + c, if a, b and c are in A.P.
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 real number x such that x2 + 1 = 0.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
Which of the following is not a statement>
The negation of the statement “101 is not a multiple of 3” is ______.
