It is important to distinguish necessary conditions (required for the consequent

Question

It is important to distinguish necessary conditions (required for the consequent to happen) from sufficient conditions (enough for the consequent to happen).

Pregnancy is required for delivery of a healthy baby, but not sufficient. Why not? There are many things that can go wrong during pregnancy.

If (Pregnant), then (deliver healthy baby). Pregnancy is a necessary condition, but not sufficient to deliver a healthy infant: there are other necessary conditions.

Notice: The definition of necessary can change as technology changes: at some point it may not be necessary to deliver a heathy infant by way of pregnancy. 'Test tube babies' still require a womb to develop, but in the future that may not always be the case. At the point that an alternative way to gestate a fetus to term exists, pregnancy would become a sufficient, but not necessary condition. Why? because an alternative would exist.

Use the reasons given in the examples (above) to decide whether the antecedent condition in each case is necessary, sufficient, necessary and sufficient, or neither. Assume the antecedent is true.

For each of the following, assume statements are true, then decide whether the antecedent condition is necessary, sufficient, neither necessary nor sufficient or both necessary and sufficient (in its relation to the stated consequence):

1. If (university is struck by asteroid) then (final exams will be cancelled).

2. If (the Butler's finger prints are found on knife stained with victim's blood), then (Butler is conclusively guilty of murdering the victim)

3. Passing calculus is required for a degree in medicine.

4. The only way (the University can avoid a tuition increase) is if (the Legislature provides enough money to cover expenses). [if (L), then only (U)]

Explanation / Answer

1. The first is a sufficient condition but not a necessary condition as there can be sundry other necessary conditions for the consequence of exam. Cancelation to take place.

2. Necessary and sufficient in order to convict the Butler for murder.

3. Necessary, but not sufficient, as there are other things that may be required to fulfill the criteria of obtaining the degree.

4. Neither necessary nor sufficient, there can be other ways to initiate the expense coverage as well as other aspects that can be factored into the result.

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