P and Q are both true.

If P is true, then Q is also true.

If P is true, then Q is false.

If Q is true, then P is also true.

Corollary

Proposition

Proof

Theorem

Lemma

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 two integers selected are even.

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

There is nothing wrong with the proof.

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

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

If P implies Q, then Q is true.

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

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

A logical consequence that has been derived 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.

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.