Advertisements
Advertisements
प्रश्न
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Advertisements
उत्तर
p ↔ q: Unit digit of an integer is zero if and only if it is divisible by 5.
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.
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.
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.
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.
Write the negation of statement:
There exists x ϵ N, x + 3 = 10
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
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.
statement are true and false? In each case give a valid reason for saying so
r : Circle is a particular case of an ellipse.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Write the negation of the following statements:
q: 9 is a multiple of 4.
Write the negation of the following statements:
r: A triangle has four sides.
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:
Mohan will be a good student if he studies hard.
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:
For all even integers x, x2 is also even.
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.
The number 100 is divisible by 3, 11 and 5.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
Write down the negation of following compound statements
All rational numbers are real and complex.
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 an odd number is odd.
Rewrite the following statements in the form of conditional statements
You will fail, if you will not study.
Identify the Quantifiers in the following statements.
There exists a real number which is not a rational number.
Identify the Quantifiers in the following statements.
There exists a even prime number other than 2.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
The negation of the statement “7 is greater than 8” is ______.
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
