If P is true, then Q is false.

If P is true, then Q is also true.

P and Q are both true.

If Q is true, then P is also true.

Lemma

Proposition

Theorem

Proof

Corollary

The proof is not verifiable - it only proves the result for two specific even integers, not all even integers.

The proof is not logical - it doesn't follow that the expression 2(x + y) is even.

The proof is not logical - it doesn't follow that the two integers selected are even.

There is nothing wrong with the proof.

If P implies Q, then Q is true.

If P and Q are true, then P implies Q.

If Q is true, and P implies Q, then P is true.

If P is true, and P implies Q, then Q is true.

A logical consequence that has been derived as part of a proof.

A previously proved theorem that can be used as part of a proof.

A hypothesis which is not yet known to be true.

A fundamental property that is always taken to be true.

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

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

There is nothing wrong with the proof.

A false conclusion has been drawn.

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

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

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

The sequence is out of order.

There is nothing wrong with the proof steps.

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

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