Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
In view of (D1), (D2), (D3) and (D4),
We observe that only statement (iv) has truth value F as the first component statement namely “every rectangle is a square” is false.
Further, in statements (i), (ii) and (v) atleast one component statement is true.
Therefore, these statements have truth value T.
Also, truth value of statement (iii) is T as both the component statements are true
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
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.
Two non-empty sets have always a non-empty intersection.
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.
This sentence is a statement.
All birds sing.
All policemen are thieves.
Write the negation of the statement:
q : For every real number x, either x > 1 or x < 1.
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.
A lady gives birth to a baby boy or a baby girl.
Write the negation of statement:
For every 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".
There is traffic jam whenever it rains.
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
r : Circle is a particular case of an ellipse.
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.
Which of the following statements are compound statements
“2 is both an even number and a prime number”
Which of the following statements are compound statements
“Ram and Rahim are friends”
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
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:
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 is a statement?
Which of the following sentences are statements? Justify
Where is your bag?
Find the component statements of the following compound statements.
Chandigarh is the capital of Haryana and U.P.
Find the component statements of the following compound statements.
Two lines in a plane either intersect at one point or they are parallel.
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
2, 3 and 6 are factors of 12
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
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 x such that x2 + 1 = 0.
Check the validity of the following statement.
p: 125 is divisible by 5 and 7.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
Which of the following is not a statement>
The negation of the statement “72 is divisible by 2 and 3” is ______.
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
