# Necessary vs Sufficient Conditions

• Necessary condition = A condition $$A$$ is said to be necessary for a condition $$B$$, iff the falsity of $$A$$, guarantees the falsity of $$B$$
• “Air is necessary for human life”
• “Without air, human beings do not live”
• “If a human is alive, then that human has air to breathe”
• In an if-then statement, the clause that follows “then” (consequent) states the necessary condition for the antecedent (clause followed by “if”)
• A necessary condition is not a sufficient condition
• All sorts of conditions may be necessary for others, but do not (by themselves) suffice or guarantee those others
• Sufficient condition = A condition $$A$$ is said to be sufficient for a condition $$B$$, iff the truth of $$A$$ guarantees the truth of $$B$$
• While air is a necessary condition for human life, it is not a sufficient condition, i.e. it does not, by itself, guarantee human life
• There are many necessary conditions for human life
• “Having four sides” is a necessary condition for a square, but that single condition by itself is not sufficient for something to be a square
• Some four sided things are not squares