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प्रश्न
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
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उत्तर
If it rains, only then the game is cancelled.
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
Show that the statement “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example.
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.
Are all circles round?
Find out the sentence are statement and are not. Justify your answer.
Is the earth round?
Write the negation of the statement:
The sun is cold.
Write the negation of the statement:
p : For every positive real number x, the number (x − 1) is also positive.
Write the negation of the statement:
r : There exists a number x such that 0 < x < 1.
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.
Negate statement:
All the students completed their homework.
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 never rains when it is cold.
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
s : If x and y are integers such that x > y, then − x < − y.
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
2 and 3 are prime numbers
Write the negation of the following statements:
p: All triangles are equilateral triangles.
Write the negation of the following statements:
q: 9 is a multiple of 4.
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”
Which of the following is a statement?
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°.
Find the component statements of the following compound statements.
`sqrt(7)` is a rational number or an irrational number.
Find the component statements of the following compound statements.
0 is less than every positive integer and every negative integer.
Find the component statements of the following compound statements.
Plants use sunlight, water and carbon dioxide for photosynthesis.
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 real numbers are rationals or irrationals.
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Rewrite the following statements in the form of conditional statements
The square of an odd number is odd.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
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.
p: 125 is divisible by 5 and 7.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “Rajesh or Rajni lived in Bangalore” 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?
