Formally, within mathematics or logic, the conjunction "and" is a two-place logical operator that yields true whenever both of its operands are true, or false whenever both of its operands are false.
In the vernacular, we use "and" to indicate conjunction. A grammatical conjunction is employed to connect two words, phrases, or clauses. Coordinating conjunctions include "and" and "or".
Formally, within mathematics or logic, the disjunction "or" is a logical operator that yields true whenever one or more of its operands is true.
In the vernacular, we use the coordinating conjuction "or" to indicate disjunction. When presented with two, or more, propositions, only one of which can be true, or when presenting alternates, opinions, or ideas of equal importance, we say either this or that/those. In other words, it could be this or it could be that/those or (often implied) it could be something else.
A disjunctive syllogism revolve around "not". The modus tollendo ponens, or MTP, is a classically valid, simple argument form:
P or Q
A is B or C or D
A is not C or D
Therefore, A is B
A fallacious disjunctive syllogism is found in the typical creationist fallacy:
Either God or Darwinian-evolution. (a false dichotomy)
Not-Darwinian-evolution. (a false premise)
Therefore, God. (a false conclusion)