Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
x > y
⇒ –x < –y (By the rule of inequality)
Thus, the given statement is true.
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
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 rhombus is a square.
Find out the sentence are statement and are not. Justify your answer.
x2 + 5 | x | + 6 = 0 has no real roots.
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 !
Give three examples of sentences which are not statements. Give reasons for the answers.
There is a complex number which is not a real number.
Both the diagonals of a rectangle have the same length.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
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 component statement of the compound statement and check whether the compound statement is true or false:
x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.
Write the negation of statement:
There exists x ϵ N, x + 3 = 10
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 never rains when 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.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Write the negation of the following statements:
q: 9 is a multiple of 4.
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.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
57 is divisible by 2 or 3.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Write down the negation of following compound statements
All rational numbers are real and complex.
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
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.
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 “Plants take in CO2 and give out O2 ” is ______.
