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: