Advertisements
Advertisements
प्रश्न
Translate the following statements into symbolic form
x and y are even integers.
Advertisements
उत्तर
p: x is an even integer.
q: y is an even integer.
p ∧ q: x and y are even integer.
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 following sentence is a statement and is not. Justify your answer.
Listen to me, Ravi !
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.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
There is a complex number which is not a real number.
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:
x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
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".
It rains only if it is cold.
Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.
Which of the following statements are compound statements
“Ram and Rahim are friends”
Write the truth value of the following statements.
(i) 9 is an even integer or 9 + 1 is even.
(ii) 2 + 4 = 6 or 2 + 4 = 7
(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.
(iv) Every rectangle is a square and every square is a rectangle
(v) The sun is a star or sun is a planet.
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.
Write the negation of the following statements:
r: A triangle has four sides.
Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day
Check the validity of the statements:
r: 100 is a multiple of 4 and 5.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
y + 9 = 7.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
2 is an even number and a prime number.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
Translate the following statements into symbolic form
Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0
Write down the negation of following compound statements
All rational numbers are real and complex.
Write down the negation of following compound statements
35 is a prime number or a composite number
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
The square of a prime number is not prime.
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 statement in above statements which is not true.
Identify the Quantifiers in the following statements.
There exists a even prime number other than 2.
Which of the following is not a statement>
Which of the following is not a negation of “A natural number is greater than zero”?
