Proof by contradiction

[thorny widget]

my intuition tells me that i can the the negation of $x \in B-C$ to prove this by contradiction.
However, i learned that i need to take the negation of $a \in C$. So my question is, am i allowed to follow my intuition here?

[sharp patrol]

Arch

[sacred charm]

To prove by contradiction you keep the same premise. The only thing is you assume the negation of the conclusion.

Here the statement is that $a \in A$ and $a \notin B-C$ $\implies a\notin C$.

[sharp patrol]

Azyrashacorki

[sacred charm]

Provided A <= B

[thorny widget]

ahhh, ok. The book i was reading told me to take the negation of P. So i thought a bit that i'm allowed to take the negation of a premise.

[sacred charm]

$(P \implies Q) \iff \lnot(P \land \lnot Q)$ is the usual statement for contradiction.

[sharp patrol]

Azyrashacorki

[thorny widget]

will keep that in mind, thanks again

i accidentally wrote $a \in C$ in the proof, when it had to be $a \notin C$. That made me also confused about this proof.

[sharp patrol]

Arch

[thorny widget]

.solved