Given the interval 3 < a < 5

We need to find the opposite interval for a.

Let us rewrite as interval.

==> a belongs to (3, 5)

Now to determine the opposite we consider that a is a real number.

Then the opposite of the interval (3, 5) is R- (3,5)

In other words, the opposite of a is all real number except the numbers in the interval (3,5)

==>** opposite a = ( -inf , 3] U [5, inf)**

In this case, the values of the number "a" have to belong to the range of real values (3 ; 5).

The interval is opened both sides, so "a" cannot be 3 or 5.

"a" is larger than 3 and it is less than 5.

To write the opposite of the given sentence means to give values to a, that are less than 3 and that are larger than 5.

So, a<3 and a>5.

To deny the given sentence, "a" has to belong to the intervals:

(-infinite;3)U(5;+infinite)