Power of Truth Tables

Whenever I get stuck on a concept or problem, whether it be from a lecture or a tutorial problem set; I find it  helpful to create a truth table. So far this course has taught me numerous new concepts and my favorite way to reinforce these new concepts is to analyse them and see why each concept is true. 

For example, understanding DeMorgan's Laws:

1. The negation of a conjunction is the disjunction of the negations.
2. The negation of a disjunction is the conjunction of the negations 

(Source: http://en.wikipedia.org/wiki/De_Morgan's_laws)

Symbolically the laws can be expressed as

1. ¬(P ∧ Q) ⇔ ¬P ∨ ¬Q

2. ¬(P ∨ Q) ⇔ ¬P ∧ ¬Q

Let's see why this is true:

1. 

2. 

The truth tables show that ¬(P ∧ Q)  is equal to ¬P ∨ ¬Q for all cases of P and Q

and that  ¬(P ∨ Q) is equal to ¬P ∧ ¬Q for all cases of P and Q.

Of course this is only a glimpse of the power of the truth table. In the future, we will be presented with exponentially longer and convoluted statements but I'm sure it's nothing that the truth table can't conquer.