The negation of the statement "The triangle i | vedclass

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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

By giving a counterexample,show that the following statement is not true.
$p:$ If all the angles of a triangle are equal,then the triangle is an obtuse-angled triangle.

If the statement $(p \vee \sim r) \rightarrow (q \wedge r)$ is false and the statement $q$ is true,then what is the truth value of statement $p$?

The truth values of $p \rightarrow r$ is $F$ and $p \leftrightarrow q$ is $F$. Then the truth values of $(\sim p \vee q) \rightarrow (p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow (\sim p \wedge q)$ are respectively:

The negation of $(p \land q) \to ((p \lor r) \to \sim q)$ is equivalent to ...

$p$ and $q$ are two logical statements. If $r: p \rightarrow (\sim p \vee q)$ has truth value false,then the truth values of $p$ and $q$ are respectively:

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