Formal Logic in Analytical Reasoning

Here are some examples of LSAT analytical reasoning rules and how you can convert them into formal logic statements. Each example shows the rule and then the corresponding conditional statement and its contrapositive.

When you are working on an LSAT game that includes conditional statements as rules convert them into symbolic IF-THEN statements and list the contra-positives. For more on how to do this see the tutorial on Formal Logic. Once you have a list of IF-THEN statements you can also combine them. More on how to do this coming soon…

A and B are not both selected together.
If A then Not B
If B then Not A

If A is selected B is also selected. (Also expressed as: A and B are always together)
If A then B
If Not B then Not A

If A is not selected B is selected.
If Not A then B
If Not B then A
This also equates to: Either A or B or Both Must be selected.

A is selected whenever B is not selected.
If Not B then A
If Not A then B
This also equates to: Either A or B or Both Must be selected.

Neither A or B is selected if C is selected.
If C then Not A AND Not B
If A OR B then Not C

If A is selected, both B and C must be selected.
If A then B AND C
If Not B OR Not C then Not A

A is selected, but only if, B is also selected.
If A then B
If Not B then Not A

Only if A is selected will B be selected.
If B then A
If Not A then Not B