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प्रश्न
Write of the statement in the form "if p, then q".
It never rains when it is cold.
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उत्तर
If it is cold, then it never rains.
संबंधित प्रश्न
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.
Find out the following sentence is a statement and is not. Justify your answer.
Listen to me, Ravi !
Find out the sentence are statement and are not. Justify your answer.
Every set is a finite set.
Find out the sentence are statement and are not. Justify your answer.
This sentence is a statement.
Give three examples of sentences which are not statements. Give reasons for the answers.
Write the negation of the statement:
The sun is cold.
Some even integers are prime.
There is a complex number which is not a real number.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
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.
Students can take Hindi or Sanskrit as their third language.
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 component statement of the compound statement and check whether the compound statement is true or false:
x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
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.
Which of the following statements are compound statements
“2 is both an even number and 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:
x + y = y + x and 29 is a prime number.
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.
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 a multiple of 6 and 9.
Check the validity of the statements:
s: 60 is a multiple of 3 or 5.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
Every square is a rectangle.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
Find the component statements of the following compound statements.
A rectangle is a quadrilateral or a 5-sided polygon.
Translate the following statements into symbolic form
2, 3 and 6 are factors of 12
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
The unit digit of an integer is 0 or 5 if it is divisible by 5.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
Which of the following is a statement?
The negation of the statement “A circle is an ellipse” is ______.
Which of the following statement is a conjunction?
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?
