The negation of the statement "The triangle i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $p$ be the statement "The triangle is an equilateral triangle".Let $q$ be the statement "The triangle is an isosceles triangle".Let $r$ be the

Vedclass · Accepted Answer

The triangle is not an equilateral or not an isosceles triangle or it is not an isosceles or it is not right angled

Vedclass · Answer

(A) Let $p$ be the statement "The triangle is an equilateral triangle".Let $q$ be the statement "The triangle is an isosceles triangle".Let $r$ be the statement "The triangle is right angled".The given statement is $(p \lor q) \land (
eg q \land r)$.We need to find the negation: $
eg((p \lor q) \land (
eg q \land r))$.Using De Morgan's Law,$
eg(A \land B) = 
eg A \lor 
eg B$,we get:$
eg(p \lor q) \lor 
eg(
eg q \land r)$.Applying De Morgan's Law again:$(
eg p \land 
eg q) \lor (q \lor 
eg r)$.This translates to: "The triangle is not equilateral and not isosceles,or the triangle is isosceles or it is not right angled".

The negation of the statement "The triangle is an equilateral or isosceles triangle and the triangle is not isosceles and it is right angled" is

Similar Questions

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If a triangle $ABC$ is equilateral,then it is isosceles.

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

Which of the following logical statements is a tautology?

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

Vedclass Test Series

Exam Paper Generator

Online Exam Module