The Many Layers of the Sufficient & Necessary Statement

I hope you are all in the midst of your LSAT prep. You may think there’s still a lot of time till the June LSAT, but if you don’t maximize the time you have, it will surely creep up on you. Today, I thought we could go over the Sufficient & Necessary statement. It’s an integral part of the exam. You will face it in the Logical Reasoning and Logic Games sections. It’s a simple concept that has many different layers. Let’s go over a few examples:

Let’s begin with the simple form of the Sufficient & Necessary statement, which I hope you are all somewhat familiar with now.

(1) If Sally goes to the mall, then she will not get her homework done and she will not be able to go out tonight.

Remember that the word “if” will introduce the sufficient condition of a Sufficient & Necessary statement. Let’s diagram:

SGM ==> not HD and not GOT

To make a contrapositive we will simply flip the conditions and negate both sides. Make sure to remember that the logical negation of an “and” is an “or.”

HD or GOT ==> not SGM

That was really simple, right? Let’s try a different type.

(2) Sally will only be able to go out tonight if she can complete all of her homework.

The trick to an “only” is to put the arrow through the only so that whatever follows the “only” is the necessary condition, and whatever precedes the “only” is the sufficient condition. The above statement written in “if/then” form would be: “If she can complete all of her homework, then Sally will be able to go out tonight.” Let’s diagram:

CAHW ==> GOT

Contrapositive:

not GOT ==> not CAHW

Remember that an “only” is not the same as “the only.” The words “the only” will introduce a sufficient condition. Let’s give that a try:

(3) The only way that Sally will be able to go out tonight is for her to do her homework.

Again, “the only” introduces the sufficient condition. The rest of the sentence is the necessary condition. The “if/then” form of this sentence is: “If Sally is able to go out tonight, then she has done her homework.” Let’s diagram:

GOT ==> DHW

Contrapositive:

not DHW ==> not GOT

See, that wasn’t too difficult right? Let’s try out one more type:

(4) Sally is able to go out tonight, unless she doesn’t finish her homework.

The trick to the “unless” is to place an arrow through it and negate what precedes it. So our “if/then” form of the sentence will be: “If Sally is not able to go out tonight, then she didn’t finish her homework.” Let’s diagram:

not GOT ==> not FHW

Contrapositive:

FHW ==> GOT