Sufficient & Necessary Conditions - Indicators

Question 1

If

Answer 1

The Rule: “if” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 2

When

Answer 2

The Rule: “when” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 3

Whenever

Answer 3

The Rule: “whenever” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 4

Where

Answer 4

The Rule: “where” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 5

Wherever

Answer 5

The Rule: “wherever” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 6

Only If

Answer 6

The Rule: “only if” introduces a necessary condition. The other part of the statement is the sufficient condition.

Question 7

Only When

Answer 7

The Rule: “only when” introduces a necessary condition. The other part of the statement is the sufficient condition.

Question 8

Only Where

Answer 8

The Rule: “only where” introduces a necessary condition. The other part of the statement is the sufficient condition.

Question 9

Only

Answer 9

The Rule: “only” introduces a necessary condition. The other part of the statement is the sufficient condition.

Question 10

Only v. the Only

Answer 10

The Rule: while “only” by itself always introduces a necessary condition, “the only” actually introduces a sufficient condition.

Question 11

If and Only If

Answer 11

The Rule: “if and only if” indicates that each variable is both a sufficient and a necessary condition. “If and only if” is diagrammed with a double arrow.

Question 12

If but Only If

Answer 12

The Rule: “if but only if” indicates that each variable is both a sufficient and a necessary condition. “If but only if” is diagrammed with a double arrow.

Question 13

All

Answer 13

The Rule: “all” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 14

Every

Answer 14

The Rule: “every” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 15

Each

Answer 15

The Rule: “each”” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 16

Any

Answer 16

The Rule: “any” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 17

People Who

Answer 17

The Rule: “people who” introduces a sufficient condition. The other part of the statement is the necessary condition.

Question 18

No Xs are Ys (i.e. “Not Both”)

Answer 18

The statement “no Xs are Ys” means that something cannot be both X and Y, or stated another way, X and Y are mutually exclusive. To diagram a “no” statement:
The Rule:

Step 1: Pick a variable (i.e. X or Y) and make it the sufficient condition.
Step 2: Negate the other variable and make it the necessary condition.

Question 19

Either X or Y (i.e. “Either/Or”)

Answer 19

The statement “either X or Y” means that at least one of X or Y must exist. To diagram an “either/or” statement:The Rule:
Step 1: Pick a variable (i.e. X or Y) and make it the necessary condition.
Step 2: Negate the other variable and make it the sufficient condition.

Question 20

Unless

Answer 20

Step 1: “Unless” introduces a necessary condition so the part of the sentence that follows “unless” will be the necessary condition.

Step 2: Negate the other part of the sentence and make it the sufficient condition.

Question 21

Without

Answer 21

Step 1: “Without” introduces a necessary condition so the part of the sentence that follows “without” will be the necessary condition.

Step 2: Negate the other part of the sentence and make it the sufficient condition.