5 tips for sharpening your logical thinking

1. Necessary conditions
Closely related to the conditional and related statements are the ideas of necessary conditions and sufficient conditions.

A necessary condition is one that must be met for a certain result to be achieved. For a smartphone not to be ruined, it must be kept out of water. Therefore “keeping a smartphone out of water” is necessary to prevent it from being ruined. The absence of virus x is necessary to have assurance that a computer does not have symptom y.

I know the objections you are raising right now, but keep reading for my further points.

2. Sufficient conditions
A sufficient condition is one that, if met, absolutely guarantees the occurrence of a certain result — that is, a result that is dependent on that condition. Dropping a smartphone into water is sufficient for ruining that phone. Doing so guarantees that the phone is ruined. The presence of virus x is a sufficient condition for a computer to exhibit symptom y.

3. Necessary but not sufficient
A condition can be necessary but not sufficient. Keeping your smartphone out of water is necessary for preventing its ruin. However, even if you do so, your smartphone could be ruined in other ways, such as being crushed by a car or dropped from a height. In the same way, even if virus x is absent from the computer, they system could still display symptom y for some other reason. Therefore, keeping a smartphone out of water, and keeping virus x off a computer are necessary but not sufficient conditions for preventing smartphone ruin or the presence of symptom y.

4. Sufficient but not necessary
Similarly, a condition can be sufficient but not necessary. Dropping the smartphone into water is a sufficient condition for ruining it. However, it is not a necessary condition for ruining it. Having virus x is a sufficient condition for symptom y. However, if symptom y can arise from other causes, having virus x is not a necessary condition.

5. Neither necessary nor sufficient
A condition can be neither necessary nor sufficient with respect to a result. To prevent the ruin of your smartphone, it is neither necessary nor sufficient that its area code begin with an even number. To prevent virus x, it is neither necessary nor sufficient that the system unit have a property tag.

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