Answer to Question #117108 in Discrete Mathematics for Priya

Question

Write the negation of the flowing statement :∃x∈R,x>3⇒x^2>9.

Answer 1

∃x∈R,x>3⇒x^2>9.

It is a quantified statement.

Rule to negate a quantified statement as follows.

∃ becomes $\forall$ followed by negation of the statement

$\forall$ becomes $\exist$ followed by negation of the statement.

Here the statement can be written as

$\exist$ p => q

Where p is x>3 and q is x^2>9.

Now p=> q is equivalent to (~p)$\lor$ q

So negation of (~ p)$\lor$ q is ~(~p$\lor$ q) = p $\land$ (~q)

So the negotiation will be

$\forall$ x∈R , x >3 and x² ≤9