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
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.
By giving a counter example, show that the following statements are not true.
q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.
Find out the sentence are statement and are not. Justify your answer.
All triangles have three sides.
Write the negation of the statement:
The earth is round.
I will not go to school.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
statement are true and false? In each case give a valid reason for saying so
t : \[\sqrt{11}\] is a rational number.
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.
It is raining or the sun is shining.
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:
p: All triangles are equilateral triangles.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
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
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Find the component statements of the following compound statements.
Number 7 is prime and odd.
Find the component statements of the following compound statements.
Chandigarh is the capital of Haryana and U.P.
Find the component statements of the following compound statements.
Two lines in a plane either intersect at one point or they are parallel.
Find the component statements of the following compound statements.
A rectangle is a quadrilateral or a 5-sided polygon.
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
Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0
Write down the negation of following compound statements
6 is divisible by 2 and 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
You will fail, if you will not study.
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.
There exists a real number which is not a rational number.
Identify the Quantifiers in the following statements.
For all real numbers x with x > 3, x 2 is greater than 9.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
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 ______.
