Advertisements
Advertisements
Question
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.
Advertisements
Solution
The given statement is of the form “q is necessary for p” where
p: Indian team wins a cricket match
q: The selection committee selects an all-rounder
Which is an equivalent form (Remark (e) 14.1.12) of “if p then q”.
So the equivalent formulation of the given statement is
“If the teams wins a cricket match then selection committee selects an all rounder.
APPEARS IN
RELATED QUESTIONS
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.
Every rhombus is a square.
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.
Is the earth round?
Find out the sentence are statement and are not. Justify your answer.
The real number x is less than 2.
Find out the sentence are statement and are not. Justify your answer.
The product of (−1) and 8 is 8.
Some even integers are prime.
I will not go to school.
All policemen are thieves.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
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.
Write the component statement of the compound statement and check whether the compound statement is true or false:
The sand heats up quickly in the sun and does not cool down fast at night.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 5.
Write of the statement in the form "if p, then q".
It is necessary to have a passport to log on to the server.
Write of the statement in the form "if p, then q".
Whenever it rains it is cold.
Check the validity of the statement:
q : 125 is a multiple of 5 and 7.
Identify the component statements and the connective in the following compound statements.
2 is a positive number or a negative number.
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:
r: A triangle has four sides.
The negation of the statement “It is raining and weather is cold.” is ______.
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
Sky is red.
Which of the following sentences are statements? Justify
Every set is an infinite set.
Find the component statements of the following compound statements.
Number 7 is prime and odd.
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.
0 is less than every positive integer and every negative integer.
Translate the following statements into symbolic form
Rahul passed in Hindi and English.
Translate the following statements into symbolic form
Either x or x + 1 is an odd integer.
Write down the negation of following compound statements
All rational numbers are real and complex.
Write down the negation of following compound statements
A triangle has either 3-sides or 4-sides.
Write down the negation of following compound statements
35 is a prime number or a composite number
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 unit digit of an integer is 0 or 5 if it is divisible by 5.
The negation of the statement “The product of 3 and 4 is 9” is ______.
