Diagramming Conditional Statements

Sufficient means

Enough

Necessary means

Required

The part of the statement that is introduced by if constitutes

The sufficient condition.

When is the temporal version of

if

Where is the spatial version of

if

These phrases can replace if or when in the if formula

Whenever | As long as

The part of the statement that is introduced by when, where, whenever, wherever, as long as constitutes the

Sufficient condition.

The part of the statement that is introduced by only if constitutes

The necessary condition.

Only when is the temporal version of

Only if. This means the part of the statement introduced by Only when constitutes the necessary condition.

Only where is the spatial version of

Only if. This means the part of the statement introduced by Only where constitutes the necessary condition.

The word “only” always ________ to a necessary condition.

Refers. This means it does not always introduce the necessary condition. It only refers to the necessary condition

The phrase the only always introduces a

sufficient condition

The part of the statement introduced by all constitutes

The sufficient condition

Each, every, and any are functionally equivalent to

All. This means that it introduces the sufficient condition.

The part of the statement introduced by no constitutes

Sufficient condition

When no introduces part of the statement, the other part of the statement is

Negated. It is also the necessary condition.

None is functionally equivalent to

No. This means that the part of the statement introduced by none constitutes the sufficient condition. Also the other part of the statement is the necessary condition and must be negated.

What is this statement equivalent to “All As are not Bs”

“No As are Bs”

What is this statement equivalent to “No As are Bs”

“All As are not Bs”

The part of the statement introduced by unless constitutes

The necessary condition. The other part of the statement must be negated and is the sufficient condition.

When unless introduced the necessary condition, the other part of the statement

is the sufficient condition and must be negated.

In the not both formula: One of the variables constitutes the sufficient condition. The other variable

must be negated and constitutes the necessary condition.

Until the temporal version of

Unless. This means that the part of the statement introduced by until constitutes the necessary condition. The other part of the statement must be negated and is the sufficient condition.

In the Either/Or formula: The negation of one of the variables constitutes the sufficient condition. The other variable

constitutes the necessary condition.

The expression “not both” implies that one of the variables must be

Absent

The expression “either….or” implies that one of the variables must be

present