Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive
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.
Two non-empty sets have always a non-empty intersection.
Find out the sentence are statement and are not. Justify your answer.
There are 35 days in a month.
Give three examples of sentences which are not statements. Give reasons for the answers.
I will not go to school.
Both the diagonals of a rectangle have the same length.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
Find the component statement of the compound statement:
All rational numbers are real and all real numbers are complex.
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.
To entry a country, you need a passport or a voter registration card.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
Write of the statement in the form "if p, then q".
It is necessary to have a passport to log on to the server.
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".
It rains only if it is cold.
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
t : \[\sqrt{11}\] is a rational number.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
Every square is a rectangle.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
Number 7 is prime and odd.
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
2, 3 and 6 are factors of 12
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
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: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
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?
