Advertisements
Advertisements
Question
Write the negation of the following statements:
x + y = y + x and 29 is a prime number.
Advertisements
Solution
Let p: x + y = y + x
And q: 29 is a prime number.
Then the conjunction in (ii) is given by p ∧ q.
Now ~ p: x + y ≠ y + x
And ~ q: 29 is not a prime number.
Therefore, using (D7), negation of p ∧ q is given by,
~ ( p ∧ q): x + y ≠ y + x or 29 is not a prime number.
APPEARS IN
RELATED QUESTIONS
Show that the following statement is true by the method of contrapositive.
p: If x is an integer and x2 is even, then x is also even.
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.
Every set is a finite set.
Find out the sentence are statement and are not. Justify your answer.
Are all circles round?
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.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
Give three examples of sentences which are not statements. Give reasons for the answers.
Some even integers are prime.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
A lady gives birth to a baby boy or a baby girl.
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 negation of statement:
For every x ϵ N, x + 3 < 10
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
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
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.
Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.
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
0 is a complex number.
Find the component statements of the following compound statements.
Chennai is in India and is the capital of Tamil Nadu.
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
Translate the following statements into symbolic form
2, 3 and 6 are factors of 12
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Write down the negation of following compound statements
35 is a prime number or a composite number
Write down the negation of following compound statements
|x| is equal to either x or – x.
Write down the negation of following compound statements
6 is divisible by 2 and 3.
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 triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
Which of the following is not a statement>
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
The negation of the statement “The product of 3 and 4 is 9” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
