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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 “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example.
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.
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.
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:
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.
Students can take Hindi or Sanskrit as their third language.
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.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
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.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
Every square is a rectangle.
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.
Two lines in a plane either intersect at one point or they are parallel.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
A triangle has either 3-sides or 4-sides.
Rewrite the following statements in the form of conditional statements
You will get a sweet dish after the dinner.
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.
Rewrite the following statements in the form of conditional statements
2b = a + c, if a, b and c are in A.P.
Identify the Quantifiers in the following statements.
For every natural number x, x + 1 is also a natural number.
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 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 “101 is not a multiple of 3” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
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?
