📘 DECK 3 — BRANCHING, BOTH / EITHER / NEITHER (COURSE-ACCURATE)

Non-hypothetical statement

A fact that is true (represented by “&”).

Words signaling non-hypotheticals

51% words such as 'most,' 'some,' 'are rarely.'

Symbolization of 'No men are butterflies'

If man → not butterfly.

Representing 'If you are one, then you are not the other'

A mutually exclusive conditional relationship.

'Both A and B' meaning

A and B are both true.

Can 'Both A and B' branch?

Yes.

'Not both A and B' meaning

At least one is false.

Diagramming 'Not both A and B'

If A → not B; If B → not A.

Possibility of not A and not B

'Neither A nor B' meaning

Not A and not B.

Can 'Neither A nor B' in the RESULT be branched?

Yes.

'Either A or B' meaning on the LSAT

At least one must be true. Possibility of both being true.

Can 'Either A or B' branched if in RESULT?

No.

Structures that allow branching

Trigger —> Not both, either

Result —> Neither, both

Structures that do NOT allow branching

Trigger —> Both, Neither

Result—> Not Both, Either

Golden branching rule

Branch only when each condition can independently occur.

Common branching mistake

Branching on 'either' when it is in the result.

Diagram for 'If A is invited, then BOTH B and C are invited'

A → B

→ C (branched).

'BOTH as the result' requires branching

Because each element (B and C) independently follows from the trigger.

Contrapositive of 'If A, then BOTH B and C'

If not B OR not C, then not A.

~ B—> ~A

~ C —>

Contrapositive of BOTH as result requirement

Yes — NOT BOTH as the trigger must be branched.

Diagram 'If O is invited, then NEITHER P nor Q is invited'

O → ~P

→ ~Q (branched).

Diagram 'If EITHER P or Q is invited, then O is not invited'

P → ~O

Q → (branched).

Diagram 'If BOTH E and F are invited, then D is not invited'

(E & F) → ¬D (NO branching).

Diagram 'If D is invited, then E and F are NOT BOTH invited'

D → ~(E & F) (NO branching).

Diagram 'If L is invited, then EITHER M or N is invited'

L → (M OR N) (NO branching).

Diagram 'If NEITHER M nor N is invited, then L is not invited'

~(M OR N) → ~L (NO branching).