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प्रश्न
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.
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उत्तर
The component statements of the given compound statement are:
1) To enter into a public library, children need an identity card from the school.
2) To enter into a public library, children need a letter from the school authorities.
The compound statement is true because both component statements are 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
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.
All triangles have three sides.
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.
Go !
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
All birds sing.
Some even integers are prime.
There is a complex number which is not a real number.
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:
All rational numbers are real and all real numbers are complex.
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.
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.
statement are true and false? In each case give a valid reason for saying so
q : The centre of a circle bisects each chord of the circle.
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Write the negation of the following statements:
q: 9 is a multiple of 4.
Write the negation of the following statements:
r: A triangle has four sides.
Rewrite the following statements in the form of conditional statements:
When you sing, my ears hurt.
Check the validity of the statements:
s: 60 is a multiple of 3 or 5.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
y + 9 = 7.
Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.
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
Rahul passed in Hindi and English.
Write down the negation of following compound statements
All prime integers are either even or odd.
Write down the negation of following compound statements
|x| is equal to either x or – x.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
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.
For all negative integers x, x 3 is also a negative integers.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
The negation of the statement “A circle is an ellipse” is ______.
The negation of the statement “72 is divisible by 2 and 3” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
The negation of the statement “101 is not a multiple of 3” is ______.
