Advertisements
Advertisements
Question
Write down the negation of following compound statements
|x| is equal to either x or – x.
Advertisements
Solution
p: |x| is equal to x.
q: |x| is equal to – x.
The negation of the above statements is
~ (p ∨ q) = (~ p ∧ ~ q): x is not equal to x and it is not equal to – x.
APPEARS IN
RELATED QUESTIONS
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.
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.
This sentence is a statement.
Find out the sentence are statement and are not. Justify your answer.
Go !
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
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.
All real numbers are complex numbers.
Both the diagonals of a rectangle have the same length.
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:
q : For every real number x, either x > 1 or x < 1.
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 is necessary to be rich in order to be happy.
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.
Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
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:
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.
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:
For all even integers x, x2 is also even.
Which of the following is a statement?
Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.
Write down the negation of following compound statements
All rational numbers are real and complex.
Write down the negation of following compound statements
All prime integers are either even or odd.
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: 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 real number x such that x2 + 1 = 0.
The negation of the statement “A circle is an ellipse” is ______.
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 ______.
The negation of the statement “101 is not a multiple of 3” is ______.
The negation of the statement “The product of 3 and 4 is 9” is ______.
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?
