This is a post in a series that focuses on the LSAT. Each post in this series contains an excerpt from our new Guide to Formal Logic on the LSAT; this focuses on if vs only if statements. If you would like to download the full guide, please use the form at the bottom of this post.

If v. Only If:  We talked about “if/then” statements in the previous section, but there’s a huge exception to the rule

If –> Then

That exception is an “only if” statement. Typically, any “if” statement suggests a sufficient condition (“if it rains, the picnic is canceled” means rain is sufficient to cancel the picnic. Many things could cancel the picnic – nuclear fallout for example – but we know one of them, for sure, is rain.) “Only if” suggests a necessary condition. (“The picnic is canceled only if it rains” means that even in the event of nuclear fallout, we’re still having a picnic, unless it also rains). You can think about “only if” statements, in regard to diagrams, as follows:

[Rest of Statement] –> Only If

Any “Only If” statement is effectively a sign that says “put this to the right of the arrow.”

Any “if” statement without the word “only” is a sign that says “put this to the left of the arrow.”

Key Words Indicating Sufficient Conditions:

“If,” Enough, Any, All, Every, None, When

Key Words Indicating Necessary Conditions:

“only if,” only, must, requires, prerequisite, “cannot without”

EXAMPLES

1. You can come skiing tomorrow only if you buy or rent skis.
2. The picnic will be canceled if it rains tomorrow

SOLUTIONS

1. Skiing –> Buy or Rent
2. Rains Tomorrow –> ~Picnic.