As we dwelve deeper and deeper into the myriad of logical equations, it helps a great deal to be able to recognize certain patterns, and to understand what, and what is not actually equivalent to one another. And so with the introduction of conjunction, disjunction, as well as negation, it becomes more and more important to know these logic laws like the back our hands!
 |
| Maybe not the approach I had in mind. |
The manipulation laws are actually quite intuitive, and don't really need that much memorization as long as you know what you're looking for. I found them to be very similar to the rules of addition/subtraction, so below are some of my analogies I came up with:
Identity: P ∧ (Q ∧ ¬ Q) ⇔ P
P + ( X + (-X) ) = P
Commutative: P ∧ Q ⇔ Q ∧ P
P + Q = Q + P
Associative: (P ∧ Q) ∧ R is ⇔ P ∧ (Q ∧ R)
(P + R) + Q = P + (Q + R)
DeMorgan's: ¬ (P ∧ Q) ⇔ ¬ P ∧ ¬ Q
-(P + Q) = -P + -Q
Naturally this doesn't cover all of the laws, such as the quantifier distributive and idempotency, but it helped me easily recognize some patterns, especially if I treat the conjunction/disjunction symbol like a plus or minus sign!
No comments:
Post a Comment