Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Here the given statement is the form p v q which has the truth value T whenever either p or q or both have the truth value T.
Hence, it is a true statement and its component statements are
p: 57 is divisible by 2. ......(False)
q: 57 is divisible by 3. ......(True)
APPEARS IN
संबंधित प्रश्न
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.
This sentence is a statement.
Find out the sentence are statement and are not. Justify your answer.
All real numbers are complex numbers.
Write the negation of the statement:
Banglore is the capital of Karnataka.
All birds sing.
Some even integers are prime.
I will not go to school.
Both the diagonals of a rectangle have the same length.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
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.
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.
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.
statement are true and false? In each case give a valid reason for saying so
p : Each radius of a circle is a chord of the circle.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Write negation of the statement
“Everyone who lives in India is an Indian”
Write the negation of the following statements:
q: 9 is a multiple of 4.
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
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:
There exists a number which is equal to its square.
Which of the following is a statement?
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
Where is your bag?
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
Find the component statements of the following compound statements.
Two lines in a plane either intersect at one point or they are parallel.
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.
Write down the negation of following compound statements
A triangle has either 3-sides or 4-sides.
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.
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 real numbers x and y, xy = yx.
Identify the Quantifiers in the following statements.
There exists a real number which is not a rational number.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
The negation of the statement “101 is not a multiple of 3” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
