Advertisements
Advertisements
Question
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Solution
The given statement is of the form “q if p”, where
p: Mohan studies hard.
q: He will be a good student.
It is an equivalent form (Remark (b) 14.1.12) of the statement “if p then q”.
So the equivalent formulation of the given statement is
“If Mohan studies hard, then he will be a good student”.
(Here, note that in p he is replaced by Mohan and in q Mohan is replaced by he)
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.
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.
There are 35 days in a month.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Write the negation of the statement:
Ravish is honest.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
Find the component statement of the compound statement:
The earth is round or the sun is cold.
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 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 negation of statement:
For every x ϵ N, x + 3 < 10
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.
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
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.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
Sum of opposite angles of a cyclic quadrilateral is 180°.
Which of the following sentences are statements? Justify
sin2x + cos2x = 0
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.
2 is an even number and a prime number.
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Identify the Quantifiers in the following statements.
There exists a real number which is not a rational number.
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
The negation of the statement “101 is not a multiple of 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?
