Exercise.

(a) Find the set of all

(b) Find the set of all

(c) Find the set of all

Give your answers as an interval or a union of disjoint intervals.

Exercise.

(a) Find the set of all ^{2-1}

(b) Find the set of all ^{2+1}

Give your answers as an interval or a union of disjoint intervals. Leave any numbers in your answers in surd form.

Exercise.

(a) Find as simple an expression as you can for _{
-1
}

(b) Supposing _{
-1
}
_{
-1
}

(c) Write down a proof that _{
1
} starting with
Let

and
Let

.

Exercise.

Consider the statement **X**, which is

and the sequence defined by (_{
)=-1
+1
}.
Prove that **X** holds for this sequence for both

**All assertions you make in your answers MUST be supported by proofs.**