The actual names of these laws are Addition, Disjunctive Syllogism and Constructive Dilemma.

Here we introduce the concept "or" symbolized by "v". So the premise "A or B" would read "A v B". With the logical concept "or" we mean that one or the other OR BOTH are true. In essence it requires neither A nor B being true for the statement "A v B" to be false. This can be tricky because often in language "or" statements are exclusive (only one can be true). This we might symbolize by saying "(A & -B) v (B & -A)". See that in law 8 below we have an example that is exclusive. Although this example still works to show law 8 , we could go a step further and say "Either I'm a boy and not a girl OR I'm a girl and not a boy" rightfully making it nonsensical for both to be true. Don't think that this exclusivity is implied by the logical statement "A v B". In "A v B" it is possible that both are true!

Example 1

*humanists believe that humans are the most important/valuable thing (usually rejecting the divine).

If God exists, humanism is not true.

If God does not exist, humanism is not true.

God exists or he does not exist.

Therefore, if God exists, humanism is not true; and if God does not exist, humanism is not true.

Therefore, either humanism is not true or humanism is not true.

Therefore, humanism is not true.

Example 2

If Jesus claimed to be God then he was either a liar or a lunatic or the lord

Jesus did claim to be God

Jesus was either a liar or a lunatic or the Lord

Jesus was not a liar or a lunatic

Jesus is the Lord

Example 3

If the butler was the murderer, then his fingerprints were on the weapon.

Either the maid or the gardener was the murderer if the butler was not.

If the gardener was the murderer, there will be blood on the garden fork.

If the maid was the murderer, then the master was killed with a kitchen knife.

The butlers fingerprints were not on the weapon.

There was no blood on the garden fork.

What can we now conclude?