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प्रश्न
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
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उत्तर
p: Hindi is the optional paper.
q: English is the optional paper.
p ∨ q: Either Hindi or English is optional paper.
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संबंधित प्रश्न
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.
Give three examples of sentences which are not statements. Give reasons for the answers.
All birds sing.
Some even integers are prime.
I will not go to school.
Both the diagonals of a rectangle have the same length.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is an irrational number.
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.
Find the component statement of the compound statement:
The sky is blue and the grass is green.
Write the component statement of the compound statement and check whether the compound statement is true or false:
Square of an integer is positive or negative.i
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.
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".
It rains only if it is cold.
statement are true and false? In each case give a valid reason for saying so
q : The centre of a circle bisects each chord of the circle.
statement are true and false? In each case give a valid reason for saying so
r : Circle is a particular case of an ellipse.
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.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
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:
For all even integers x, x2 is also even.
Which of the following sentences are statements? Justify
A triangle has three sides.
Which of the following sentences are statements? Justify
Sky is red.
Find the component statements of the following compound statements.
Chennai is in India and is the capital of Tamil Nadu.
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.
Two lines in a plane either intersect at one point or they are parallel.
Find the component statements of the following compound statements.
A rectangle is a quadrilateral or a 5-sided polygon.
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.
Write down the negation of following compound statements
All real numbers are rationals or irrationals.
Write down the negation of following compound statements
35 is a prime number or a composite number
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
You will fail, if you will not study.
Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.
Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.
Identify the Quantifiers in the following statements.
There exists a triangle which is not equilateral.
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 statement in above statements which is not true.
The negation of the statement “The product of 3 and 4 is 9” is ______.
