मराठी

Statement Are True and False? in Each Case Give a Valid Reason for Saying So R : Circle is a Particular Case of an Ellipse.

Advertisements
Advertisements

प्रश्न

 statement are true and false? In each case give a valid reason for saying so

r : Circle is a particular case of an ellipse.

Advertisements

उत्तर

 Equation of an ellipse: \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]

If we put a = b = 1, then we obtain \[x^2 + y^2 = 1\]

, which is an equation of a circle. Therefore, a circle is a particular case of an ellipse.

Thus, the statement is true.

 
 
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Show that the statement “For any real numbers a and ba2 = 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.

Is the earth round?


Write the negation of the statement:

 Ravish is honest.


Write the negation of the statement:

 The earth is round.


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 sky is blue and the grass is green.


For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

 To entry a country, you need a passport or a voter registration card.


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  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.


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.


Which of the following statements are compound statements 

“2 is both an even number and a prime number”


Translate the following statements in symbolic form

Tigers are found in Gir forest or Rajaji national park.


Rewrite the following statements in the form of conditional statements:

Mohan will be a good student if he studies hard.


Rewrite the following statements in the form of conditional statements:

When you sing, my ears hurt.


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:
For all even integers x, x2 is also even.


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

Every set is an infinite set.


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.

Chennai is in India and is the capital of Tamil Nadu.


Find the component statements of the following compound statements.

The number 100 is divisible by 3, 11 and 5.


Write the component statements of the following compound statements and check whether the compound statement is true or false.

All living things have two eyes and two legs.


Translate the following statements into symbolic form

Rahul passed in Hindi and English.


Write down the negation of following compound statements

All real numbers are rationals or irrationals.


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

|x| is equal to either x or – x.


Write down the negation of following compound statements

6 is divisible by 2 and 3.


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.


Rewrite the following statements in the form of conditional statements

The square of a prime number is not prime.


Form the biconditional statement p ↔ q, where
p: The unit digit of an integer is zero.
q: It is divisible by 5.


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 triangle which is not an isosceles triangle.


Which of the following is a statement?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×