Advertisements
Advertisements
Question
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.
Advertisements
Solution
The argument used to check the validity of the given statement is false because it is given in the argument that x2 = π 2 is irrational and therefore x = π is irrational; however, according to the statement, x is rational.
APPEARS IN
RELATED QUESTIONS
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.
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.
Go !
Find out the sentence are statement and are not. Justify your answer.
The product of (−1) and 8 is 8.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
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:
To enter into a public library children need an identity card from the school or a letter from the school authorities.
Write the negation of statement:
There exists x ϵ N, x + 3 = 10
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 rains only if it is cold.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
statement are true and false? In each case give a valid reason for saying so
s : If x and y are integers such that x > y, then − x < − y.
statement are true and false? In each case give a valid reason for saying so
t : \[\sqrt{11}\] is a rational number.
Write the negation of the following statements:
q: 9 is a multiple of 4.
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:
A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
y + 9 = 7.
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
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.
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.
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 fail, if you will not study.
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.
Identify the Quantifiers in the following statements.
There exists a triangle which is not equilateral.
Identify the Quantifiers in the following statements.
There exists a real number which is not a rational number.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
The negation of the statement “7 is greater than 8” 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 ______.
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?
