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प्रश्न
Translate the following statements into symbolic form
Rahul passed in Hindi and English.
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उत्तर
p: Rahul passed in Hindi.
q: Rahul passed in English
p ∧ q: Rahul passed in Hindi and English.
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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.
All real numbers are complex numbers.
Give three examples of sentences which are not statements. Give reasons for the answers.
Some even integers are prime.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is an irrational number.
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.
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:
All rational numbers are real and all real numbers are not complex.
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 = 4.
Write the negation of statement:
There exists x ϵ N, x + 3 = 10
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
p : Each radius of a circle is a chord of the circle.
Which of the following statements are compound statements
“9 is neither an even number nor a prime number”
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
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°.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Translate the following statements into symbolic form
x and y are even integers.
Write down the negation of following compound statements
All rational numbers are real and complex.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.
Identify the Quantifiers in the following statements.
There exists a triangle which is not equilateral.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
Which of the following is not a statement>
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “7 is greater than 8” is ______.
The negation of the statement “72 is divisible by 2 and 3” is ______.
The negation of the statement “101 is not a multiple of 3” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
Which of the following statement is a conjunction?
