Necessary and Sufficient Conditions

# Necessary and Sufficient Conditions - Todays Topics(11/18 I...

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3/4/11 Today’s Topics (11/18) I. Necessary Conditions II. Sufficient Conditions III. Necessary and Sufficient Conditions IV. Symbolizing Sufficient Conditions V. Symbolizing Necessary Conditions VI. Symbolizing Necessary and Sufficient Conditions Propositional Logic and Everyday

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3/4/11 I. Necessary Conditions A necessary condition for the occurrence of an event is one without which the event cannot occur. Examples: Ø A person cannot survive without being able to breathe. So, being able to breathe is a necessary condition for the
3/4/11 II. Sufficient Conditions A sufficient condition for the occurrence of an event is one that guarantees that the event occurs. Examples: Ø Being a square is a sufficient condition for being a rectangle.

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3/4/11 III. Necessary and Sufficient Conditions Compared A condition can be necessary for an event without being sufficient: § Being at least 18 is a necessary condition for being able to vote legally in the U.S., but it is not a sufficient condition. One must also be a citizen, have a free criminal record, and be registered to vote. § Being a rectangle is a necessary condition for being a square. But it is
3/4/11 III. Necessary and Sufficient Conditions Compared Sometimes, a condition or set of conditions can be both necessary and sufficient for another condition. § Having exactly four right angles and four equal sides where each side is a line segment is both necessary and sufficient for being a square.

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Necessary and Sufficient Conditions - Todays Topics(11/18 I...

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