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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Identify the antecedent and the consequent in each of the following statements.
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(a) If n is an integer, then 2n is an even number.
(b) You can work here only if you have a college degree.
(c) The car will not run whenever you are out of gas.
(d) Continuity is a necessary condition for differentiability. One way to visualize an implication R ⇒ S is to picture two sets R and S, with R inside S. Figure 1 shows several objects of different shapes. Some are round and some are not round. Some are solid and some are not solid. Objects that are round are in set R and objects that are solid are in set S.

We see that the relationship between R and S in Figure 1 can be stated in several equivalent ways:
• If an object is round (R), then it is solid (S).
• An object is solid (S) whenever it is round (R).
• An object is solid (S) provided that it is round (R).
• Being round (R) is a sufficient condition for an object to be solid (S). (It is sufficient to know that an object is round to conclude that it is solid.)
• Being solid (S) is a necessary condition for an object to be round (R). (It is necessary for an item to be solid in order for it to be round.)
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