Advertisements
Advertisements
Question
Find out the sentence are statement and are not. Justify your answer.
x2 + 5 | x | + 6 = 0 has no real roots.
Solution
x2 + 5 | x | + 6 = 0 has no real roots.
It is a true declarative sentence, so it is a statement.
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.
By giving a counter example, show that the following statements are not true.
p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
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.
Is the earth round?
Write the negation of the statement:
Ravish is honest.
Write the negation of the statement:
The earth is round.
I will not go to school.
Both the diagonals of a rectangle have the same length.
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.
Find the component statement of the compound statement:
25 is a multiple of 5 and 8.
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 component statement of the compound statement and check whether the compound statement is true or false:
The sand heats up quickly in the sun and does not cool down fast at night.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 = 4.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
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".
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.
statement are true and false? In each case give a valid reason for saying so
r : Circle is a particular case of an ellipse.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Write the negation of the following statements:
x + y = y + x and 29 is a prime number.
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Find the component statements of the following compound statements.
Number 7 is prime and odd.
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
A number is either divisible by 2 or 3.
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
6 is divisible by 2 and 3.
Rewrite the following statements in the form of conditional statements
The square of a prime number is not prime.
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 triangle which is not equilateral.
Identify the Quantifiers in the following statements.
For all real numbers x and y, xy = yx.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
Which of the following is the conditional p → q?
Which of the following statement is a conjunction?