The proof is not sequential: some steps depend on information that comes later.

A false conclusion has been drawn.

There are no logical deductions in this proof: it is simply a set of facts or assumptions that doesn't tell us anything new.

There is nothing wrong with the proof.

The proof is not verifiable, because it is impossible to verify the result of each individual sum.

The proof is not verifiable, because there are an infinite number of sums that need to be evaluated in order to verify it.

The final sentence does not follow as a logical consequence of the previous statement.

The proof does not follow logically, because the theorem is not true.

There is nothing wrong with the proof.

We cannot make assumptions about the truth values of A and B.

There is nothing wrong with the proof steps.

Statement 3 does not follow as a logical consequence of the previous statements.

The sequence is out of order.

We have shown that P(x) is true for x = 1, 2, 3, 4; therefore we can deduce it is true for all other positive integers.

Since we know that x = a + b and f(x) = x^2, we can also say that f(x) = (a + b)^2.

By Theorem n, which was proved previously, we know that P(x) is true for all positive integers.

Since we know that P_1 is true, and that P_1 \rightarrow P_2, we can also say that P_2 is true.

9

8

10

0

1

temp >= 20 || temp <= 25 && !raining

20 < temp < 25 && !raining

temp >= 20 || temp <= 25 || !raining

temp >= 20 && temp <= 25 && !raining

temp <= 20 && temp <= 25 && !raining

temp >= 20 && temp <= 25 || !raining

5, 4

5, 5

3, 3

4, 4

4, 3