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प्रश्न
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
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उत्तर
p: Hindi is the optional paper.
q: English is the optional paper.
p ∨ q: Either Hindi or English is optional paper.
APPEARS IN
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 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.
Two non-empty sets have always a non-empty intersection.
Find out the sentence are statement and are not. Justify your answer.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
x2 + 5 | x | + 6 = 0 has no real roots.
Find out the sentence are statement and are not. Justify your answer.
Mathematics is difficult.
Find out the sentence are statement and are not. Justify your answer.
The product of (−1) and 8 is 8.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Write the negation of the statement:
Ravish is honest.
Write the negation of the statement:
The earth is round.
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.
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.
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.
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.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
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.
Write of the statement in the form "if p, then q".
It never rains when it is cold.
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.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
Write negation of the statement
“Everyone who lives in India is an Indian”
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:
Ramesh will get dessert only if he eats his dinner.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
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
0 is a complex number.
Which of the following sentences are statements? Justify
15 + 8 > 23
Find the component statements of the following compound statements.
Number 7 is prime and odd.
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.
A rectangle is a quadrilateral or a 5-sided polygon.
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.
Translate the following statements into symbolic form
Rahul passed in Hindi and English.
Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.
Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Identify the Quantifiers in the following statements.
For every natural number x, x + 1 is also a natural number.
