Advertisements
Advertisements
प्रश्न
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Advertisements
उत्तर
Let p: ABC is an equilateral triangle
And q: Each interior angle of triangle ABC is 60°
Then the given statement in symbolic form is p ↔ q.
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
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.
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.
The cat pussy is black.
Find out the sentence are statement and are not. Justify your answer.
There are 35 days in a month.
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:
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:
All rational numbers are real and all real numbers are not complex.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 4.
Negate statement:
All the students completed their homework.
Write of the statement in the form "if p, then q".
There is traffic jam whenever it rains.
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".
Whenever it rains it is cold.
Write of the statement in the form "if p, then q".
It never rains when it is cold.
Check the validity of the statement:
r : 60 is a multiple of 3 or 5.
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.
Translate the following statements in symbolic form
2 and 3 are prime numbers
Write negation of the statement
“Everyone who lives in India is an Indian”
Write the negation of the following statements:
r: A triangle has four sides.
Write the negation of the following statements:
x + y = y + x and 29 is a prime number.
Rewrite the following statements in the form of conditional statements:
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
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 sentences are statements? Justify
A triangle has three sides.
Find the component statements of the following compound statements.
Chennai is in India and is the capital of Tamil Nadu.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
All living things have two eyes and two legs.
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
The square of an odd number is odd.
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 triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Identify the Quantifiers in the following statements.
There exists a triangle which is not equilateral.
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.
For all real numbers x with x > 3, x 2 is greater than 9.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
