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. - Mathematics

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?
पाठ 31: Mathematical reasoning - Exercise 31.6 [पृष्ठ २९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 31 Mathematical reasoning
Exercise 31.6 | Q 7.3 | पृष्ठ २९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Show that the following statement is true by the method of contrapositive.

pIf x is an integer and x2 is even, then x is also even.


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.

All real numbers are complex numbers.


Find out the sentence are statement and are not. Justify your answer.

The product of (−1) and 8 is 8.

 

Write the negation of the statement:

 It rained on July 4, 2005.


Write the negation of the statement:

 Ravish is honest.


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 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:

 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:

 x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.


Write of the statement in the form "if p, then q". 

There is traffic jam whenever it rains.


Write of the statement in the form "if p, then q". 

 Whenever it rains it is cold.


Write the negation of the following statements:
x + y = y + x and 29 is a prime number.


Translate the following biconditional into symbolic form:
“ABC is an equilateral triangle if and only if its each interior angle is 60°”


Check the validity of the statements:
r: 100 is a multiple of 4 and 5.


Check the validity of the statements:
s: 60 is a multiple of 3 or 5.


Which of the following is a statement?


Which of the following sentences are statements? Justify

A triangle has three sides.


Which of the following sentences are statements? Justify

0 is a complex number.


Which of the following sentences are statements? Justify

Sky is red.


Find the component statements of the following compound statements.

Number 7 is prime and odd.


Find the component statements of the following compound statements.

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


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

2, 3 and 6 are factors of 12


Write down the negation of following compound statements

x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.


Write down the negation of following compound statements

All prime integers are either even or odd.


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

2b = a + c, if a, b and c are in A.P.


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.


Identify the Quantifiers in the following statements.

There exists a even prime number other than 2.


The negation of the statement “101 is not a multiple of 3” is ______.


Which of the following is the conditional p → q?


Which of the following statement is a conjunction?


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×