Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
The given statements are not negation of each other because the negation of " \[a + b = b + a\] is true for every real number a and b" is "There exist real numbers a and b for which \[a + b \neq b + a\] .
APPEARS IN
संबंधित प्रश्न
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.
There are 35 days in a month.
Write the negation of the statement:
The sun is cold.
Both the diagonals of a rectangle have the same length.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
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:
To enter into a public library children need an identity card from the school or a letter from the school authorities.
Negate statement:
All the students completed their homework.
Negate of the statement :
There exists a number which is equal to its square.
Write of the statement in the form "if p, then q".
There is traffic jam whenever it rains.
Write of the statement in the form "if p, then q".
It never rains when it is cold.
Which of the following statements are compound statements
“9 is neither an even number nor a prime number”
Translate the following statements in symbolic form
2 and 3 are prime numbers
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
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:
p: All triangles are equilateral triangles.
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:
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°”
Which of the following sentences are statements? Justify
Every set is an infinite set.
Which of the following sentences are statements? Justify
Where is your bag?
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.
0 is less than every positive integer and every negative integer.
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
x and y are even integers.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
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
2b = a + c, if a, b and c are in A.P.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
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.
For every natural number x, x + 1 is also a natural number.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
The negation of the statement “7 is greater than 8” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
Which of the following statement is a conjunction?
