Proof that $B \land ( B \lor C) = B$? In my logic design exam today I was given this question:


  Show that:
  $$ B  \land ( B \lor C) = B $$


It's asking for a proof for this expression. Could someone please explain how such expression can be proven? I'm not that good at Boolean algebra but I believe that it's in the simplest form.
A truth table will show it 

B    C    B or C    B and (B or C)

T    T      T            T
T    F      T            T
F    T      T            F
F    F      F            F
Distribute out expression, and you're left with B and B = B or B and C. so that should imply B.

$B \wedge (B \lor C) = (B\wedge B) \lor (B\wedge C )= B \lor (B\wedge C ) = B$