Advertisements
Advertisements
प्रश्न
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
Go !
Find out the sentence are statement and are not. Justify your answer.
Mathematics is difficult.
Write the negation of the statement:
The sun is cold.
Both the diagonals of a rectangle have the same length.
Find the component statement of the compound statement:
All rational numbers are real and all real numbers are complex.
Write the negation of statement:
For every x ϵ N, x + 3 < 10
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
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
s : If x and y are integers such that x > y, then − x < − y.
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.
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Write the negation of the following statements:
p: All triangles are equilateral triangles.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
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 equal to its square.
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Which of the following is a statement?
Which of the following sentences are statements? Justify
Every square is a rectangle.
Which of the following sentences are statements? Justify
Sum of opposite angles of a cyclic quadrilateral is 180°.
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
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.
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
Rahul passed in Hindi and English.
Translate the following statements into symbolic form
x and y are even integers.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
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 real numbers are rationals or irrationals.
Write down the negation of following compound statements
A triangle has either 3-sides or 4-sides.
Write down the negation of following compound statements
All prime integers are either even or odd.
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: The unit digit of an integer is zero.
q: It is divisible by 5.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
The negation of the statement “7 is greater than 8” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
