Sufficient & Necessary Conditions Diagramming Rules

Question 1

If

Answer 1

Introduces A Sufficient Condition

Question 2

When/Whenever

Answer 2

Introduces A Sufficient Condition

Question 3

Where/Wherever

Answer 3

Introduces A Sufficient Condition

Question 4

THE Only

Answer 4

Introduces A Sufficient Condition

Question 5

Only

Answer 5

Introduces A Necessary Condition

Question 6

Only If

Answer 6

Introduces A Necessary Condition

Question 7

Only When

Answer 7

Introduces A Necessary Condition

Question 8

Only Where

Answer 8

Introduces A Necessary Condition

Question 9

If AND Only If

Answer 9

Introduces Both Sufficient AND Necessary Conditions

Both Variables MUST Exist Together

ie; Marcy will go to school if AND only if PB goes to school.

This tells us both “If M @ school then PB @ school” AND “If PB @ school then M @ School) and is diagrammed with a double-sided arrow:
(M @ School PB @ School) or
(PB @ School M @ School)

Question 10

If BUT Only If

Answer 10

Introduces Both Sufficient AND Necessary Conditions

Both Variables MUST Exist Together

ie; Marcy will go to school if BUT only if PB goes to school.

This tells us both “If M @ school then PB @ school” AND “If PB @ school then M @ School) and is diagrammed with a double-sided arrow:
(M @ School PB @ School) or
(PB @ School M @ School)

Question 11

All/Every/Each/Any

Answer 11

Introduce a Sufficient Condition and are all diagrammed the same way.

ie; All/Every/Each/Any Humans are Mammals is diagrammed as H —> M.

Question 12

People Who

Answer 12

Introduces a Sufficient Condition.

ie; People who get pregnant are female.
P —> F

Question 13

No

Answer 13

Something cannot be both X & Y.

X & Y cannot both exist at the same time, they are mutually exclusive.

Question 14

Rules for Diagramming No

Answer 14

Step 1: Pick a variable (X, Y, etc.) and make it the sufficient condition.

Step 2: The other variable becomes the necessary condition and is negated.

ie; No fish are mammals.
(F —> Not M) or (M —> Not F)

Note: It is possible that neither exists at the same time, meaning (Not F & Not M).

Question 15

Not Both

Answer 15

Something cannot be both X & Y.

X & Y cannot both exist at the same time, they are mutually exclusive.

Question 16

Rules for Diagramming Not Both

Answer 16

Diagrammed exactly like No.

ie; One cannot be both in LA and NY at the same time.
(in LA —> Not in NY) or (in NY —> Not in LA)

Note: It is possible that neither exists at the same time, meaning (Not in LA & Not in NY).

Question 17

Either/Or

Answer 17

At least one of the variables MUST exist, both may also exist.

Question 18

Rules for Diagramming Either/Or

Answer 18

Rule #1: Pick a variable (X, Y, etc.) and make it the necessary condition.

Rule #2: The other variable becomes the sufficient condition and is negated.

ie; Either love me or leave me.
(Not Love Me —> Leave Me) or
(Not Leave Me —> Love Me)

Question 19

Unless

Answer 19

Introduces a Necessary Condition.

Question 20

Rules for Diagramming Unless

Answer 20

Rule #1: The statement after unless is the necessary condition.

Rule #2: The other statement/part of the sentence is the sufficient condition and is negated.

ie; A person cannot win the lottery unless they buy a ticket.
(Win Lottery —> Buy Ticket)

Question 21

Without

Answer 21

Introduces a Necessary Condition.

Question 22

Rules for Diagramming Without

Answer 22

Diagrammed exactly like unless.

ie; Without oxygen, you cannot have fire.
F —> O

Question 23

Until

Answer 23

Introduces a Necessary Condition

Question 24

Rules for Diagramming Until

Answer 24

Diagrammed exactly like unless and without.

ie; Until a gov’t cares for its needy, it is not humane.
(Humane —> Care for Needy)
or
A person cannot legally drink until they are 21 y/o.
(Drink Legally —> 21 y/o)

Question 25

Rules for Diagramming If and Only If

Answer 25

Rule #1: Pick a variable and make it the sufficient or necessary condition.

Rule #2: The remaining variable becomes the remaining condition (sufficient or necessary).