English

Form the biconditional statement p ↔ q, wherep: A triangle is an equilateral triangle.q: All three sides of a triangle are equal. - Mathematics

Advertisements
Advertisements

Question

Form the biconditional statement p ↔ q, where
p: A triangle is an equilateral triangle.
q: All three sides of a triangle are equal.

Sum
Advertisements

Solution

p ↔ q: A triangle is an equilateral triangle if and only if all three sides of triangle are equal.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Mathematical Reasoning - Exercise [Page 263]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 14 Mathematical Reasoning
Exercise | Q 8.(iii) | Page 263

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.

Two non-empty sets have always a non-empty intersection.


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.

 Are all circles round?


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

 All triangles have three sides.


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

 x2 + 5 | x | + 6 = 0 has no real roots.


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

 Mathematics is difficult.


Write the negation of the statement:

 The earth is round.


 I will not go to school.


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.

 

Find the component statement of the compound statement:

All rational numbers are real and all real numbers are complex.


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 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.


Which of the following statements are compound statements 

“9 is neither an even number nor a prime number”


Write the negation of the following statements:
p: All triangles are equilateral triangles.


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


Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4


Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.


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


Which of the following is a statement?


Which of the following sentences are statements? Justify

Every set is an infinite set.


Which of the following sentences are statements? Justify

y + 9 = 7.


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.

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


Find the component statements of the following compound statements.

Chandigarh is the capital of Haryana and U.P.


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

A number is either divisible by 2 or 3.


Write down the negation of following compound statements

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


Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.


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.

For all negative integers x, x 3 is also a negative integers.


Check the validity of the following statement.
q: 131 is a multiple of 3 or 11


The negation of the statement “Plants take in CO2 and give out O2 ” is ______.


Which of the following is the conditional p → q?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×