How to prove B from a premise in which B does not occur using natural deduction?

Question

I am preparing for my first logic exam and in the test examples I've come across the following question:

Prove by natural deduction:

B from premise A ∧ ¬A

I am unsure how to proceed in formulating this proof as B does not bear any relation to the premise. Does someone know how to proceed with such a proof? What can I assume about B's relation to the premise?

Answer 1

Here is a proof in the logic software program Fitch:

Answer 2

Here are the questions:

I am unsure how to proceed in formulating this proof as $B$ does not bear any relation to the premise. Does someone know how to proceed with such a proof? What can I assume about B's relation to the premise?

Since $B$ does not appear in the premises it may be that the premises are contradictory. From a contradiction anything follows (in particular, $B$). If one can show that the premises are contradictory, then one can use the rule of explosion (x) or ex falso quodlibet to derive $B$.

This is actually the case since $A$ and $¬A$ are contradictory. Here is a proof of $A ∧ ¬A ∴ B$ which you can enter in this proof checker to verify for yourself: