Formal Logic

“unless”/“without“/“until”

signal n-term in conditional relationship, replace with "if not" and add to start of sentence, treat "unless" as the n-term by replacing it with the arrow and negating the s-term

example of necessary terms

then, requires, gurantees, must, necessary, bound to lead to, destined to, only/only if, results in, produces, sure to, always, depends on

examples of sufficient terms

if, all, any, every, each, when, whenever, wherever, the only

how to form a contrapositive

reverse s- and n-term, negate both, change "and" to "or"/"or" to "and"

“or”

at least one of the terms (the first or the second or both) is needed for a sufficient condition to trigger a result or for a necessary condition to be fulfilled

“and”

both terms are needed for a sufficient condition to trigger a result or for a necessary condition to be fulfilled

contrapositive

another way to describe the same logical relationship of sufficiency and necessity by stating that if we know that the necessary term is not true, then the sufficient cannot be true. This is because it is impossible for the sufficient term to be true without the necessary term.

necessary term

must be true if the sufficient term is triggered. This is the logical “result of” or “requirement for” the sufficient term.

sufficient term

if true, is enough to absolutely guarantee the necessary term. This is the “trigger” for the necessary term

conditional statement

contains two parts: sufficient and necessary