Sufficient & Necessary Questions - - Question 19

Only an expert in some branch of psychology could understand why Patrick is behaving irrationally. But no expert is c...

Ben August 15, 2019

Only in the passage

I thought "Only" introduces a sufficient condition and "the only" introduces a necessary condition. Why in the example is Expert the necessary condition?

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Irina August 15, 2019

@ Ben,

Great question. It is the other way around - "only" or "only if" typically introduces a necessary condition, and "the only" introduces a sufficient condition. "If and only if" introduces both.

Only an expert could understand:

IF understand THEN an expert
IF NOT an expert THEN not understand

Compare it to:

The only president to serve two nonconsecutive terms is Grover Cleveland.

IF nonconsecutive terms THEN Grover Cleveland
IF NOT Grover Cleveland THEN NOT nonconsecutive terms.

And compare it to:

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

IF sum divisible THEN number divisible
IF number divisible THEN sum divisible

Does this make sense?

Let me know if you have any further questions.