I'm struggling with proving that theese 2 boolean functions are equivalent.
$$(a \vee b) \equiv c$$ $$(a \equiv c) \equiv (b \Rightarrow a)$$
I'm not allowed to use truth tables or Vienn diagrams.
My teacher told me that I need to get one of the formulas to look like the other one, but I struggle with that. Here's that I got so far:
$$(a \lor b) \equiv c \\ \equiv ((a \lor b) \land c) \lor (\lnot (a \lor b) \land \lnot c) \\ \equiv (a \land c \lor a \land b) \lor (\lnot a \land \lnot b \land \lnot c) \\ \equiv a \land c \lor a \land b \lor \lnot a \land \lnot b \land \lnot c \\ \equiv a \land (b \lor c) \lor \lnot a \land (\lnot b \land \lnot c)$$
I don't know what to do next, I'm not sure how to make it look like the other formula at this point.
Edit: first formula was wrong, sorry.