Advertisements
Advertisements
Question
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
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
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
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.
Are all circles round?
Find out the sentence are statement and are not. Justify your answer.
Every rhombus is a square.
Find out the sentence are statement and are not. Justify your answer.
All real numbers are complex numbers.
All birds sing.
There is a complex number which is not a real number.
All policemen are thieves.
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 negation of statement:
For every x ϵ N, x + 3 < 10
Write the negation of statement:
There exists x ϵ N, x + 3 = 10
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
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 the negation of the following statements:
r: A triangle has four sides.
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.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
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
A number is either divisible by 2 or 3.
Write down the negation of following compound statements
All rational numbers are real and complex.
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
Rewrite the following statements in the form of conditional statements
2b = a + c, if a, b and c are in A.P.
Identify the Quantifiers in the following statements.
For all real numbers x with x > 3, x 2 is greater than 9.
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “A circle is an ellipse” is ______.
The negation of the statement “7 is greater than 8” is ______.