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प्रश्न
Write of the statement in the form "if p, then q".
It rains only if it is cold.
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उत्तर
If it rains, then it is cold.
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संबंधित प्रश्न
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
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 real numbers are complex numbers.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Write the negation of the statement:
It rained on July 4, 2005.
All birds sing.
I will not go to school.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
There exist real numbers a and b for which a + b = b + a.
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:
The earth is round or the sun is cold.
Find the component statement of the compound statement:
All rational numbers are real and all real numbers are complex.
Find the component statement of the compound statement:
25 is a multiple of 5 and 8.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
A lady gives birth to a baby boy or a baby girl.
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 component statement of the compound statement and check whether the compound statement is true or false:
The sand heats up quickly in the sun and does not cool down fast at night.
Negate statement:
All the students completed their homework.
Write of the statement in the form "if p, then q".
It is necessary to have a passport to log on to the server.
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
r : Circle is a particular case of an ellipse.
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:
Mohan will be a good student if he studies hard.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Which of the following sentences are statements? Justify
y + 9 = 7.
Which of the following sentences are statements? Justify
Every square is a rectangle.
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.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
35 is a prime number or a composite number
Rewrite the following statements in the form of conditional statements
You will get a sweet dish after the dinner.
Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.
Which of the following is not a statement>
