Necessary and Sufficient Conditions

By
Greg Smith

Necessary and Sufficient conditions are what make up the two sides of an IF THEN statement.

You can find IF THEN statements with necessary and sufficient conditions in both the Logic Games and Logical Reasoning sections of the LSAT.
Here’s another look at our IF THEN statements…
IF A then B
A is our sufficient condition – if we have A then we will always have B or in other words A is sufficient to know that we must have B
B is our necessary condition – B is necessary or required in order to have A. So if we do not have B then we will not have A. We see this in our contra-positive IF not B then not A.

Here is a basic logical reasoning style examples of these conditions:
The local theatre will only produce a new play if it has seen previous success in another theatre. My play has never been successful in another theatre, therefore my play will not be produced by the local theatre.

The necessary condition here is that a play “has seen previous success in another theatre”
In the absence of this condition we do not achieve our other condition – the sufficient one.
The sufficient condition is “the local theatre producing a play”

If I tell you that Bob’s play was produced by the local theatre, then you know for sure that Bob’s play has seen previous success in other theatres as that is a requirement for this local theatre to produce it. So being produced locally is sufficient to know that the play saw success in another theatre.
Another way to look at necessary and sufficient conditions is this:

I require air to live. (air is a necessary condition for my life)
If I am alive tomorrow then you know I have air. (being alive is sufficient for you to know that I have air)

Here’s another example of a logical reasoning style question that uses necessary and sufficient conditions/formal logic to get to the correct answer.

Whenever you encounter a logical reasoning question that uses the following words, it can be a good idea to diagram some of the statements in the argument out. You only need to do this if you are having trouble understanding the logic of the argument, often it is easy to understand and faster without a diagram. But if you’re struggling, a quick diagram can help a lot.

The words that make for easier diagrams are:
IF THEN
ONLY IF
UNLESS
IF BUT ONLY IF
IF AND ONLY IF

The example with Miley Cyrus and LSAT conditional statements above is a great example of when diagramming helps.

Also here’s some more articles on formal logic & conditional reasoning.

For complete coverage of this topic and tonnes of practice questions explained. Check out our LSAT Prep Course.

February 18, 2011

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