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.
p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
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.
All triangles have three sides.
Find out the sentence are statement and are not. Justify your answer.
This sentence is a statement.
Write the negation of the statement:
Ravish is honest.
All birds sing.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
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.
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.
Negate statement:
All the students completed their homework.
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".
It never rains when it is cold.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
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.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
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
Identify the quantifiers and write the negation of the following statements:
There exists a number which is a multiple of 6 and 9.
Which of the following sentences are statements? Justify
0 is a complex number.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.
Translate the following statements into symbolic form
A number is either divisible by 2 or 3.
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
All prime integers are either even or odd.
Write down the negation of following compound statements
|x| is equal to either x or – x.
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.
There exists a triangle which is not equilateral.
Identify the Quantifiers in the following statements.
For every natural number x, x + 1 is also a natural number.
Identify the Quantifiers in the following statements.
There exists a statement in above statements which is not true.
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 “Rajesh or Rajni lived in Bangalore” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
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?
