Exercise.
(a) Write down the negation of the following
statements in such a way as there are no not
signs in your answer. Logical symbols,
A:
B:
(b) Now interpret the domain
(c) Attempt to write down proofs of your assertions in part (b).
Note: your proof will ultimately rely on obvious
properties
of the order relation obvious
for the reason.) Your work will be marked on
whether you have the correct structure for a proof. Use the following
model answers
for case (iii) as a model.
Answer for case (iii)
A:
Proof.
Subproof.
Let
Subproof.
Let
Then
So
So
B:
Proof.
Subproof.
Let
Subproof.
Let
Subproof.
Suppose
Subproof.
Let
Then
So
Then
So
So
Exercise.
Consider the following statement about a sequence (
C:
(a) Write down the negation of this statement.
(b) Decide whether the statement
C is true or false, and prove your assertion for
(c) Do the same for