Implies

Implies[p,q]

represents the logical implication .

Details

Examples

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Basic Examples  (2)

Enter using =>:

Scope  (4)

Certain arguments automatically simplify:

Expand in terms of And, Or, and Not:

Do symbolic simplification:

TraditionalForm formatting:

Applications  (3)

Use Implies to combine two regions:

Symbolic reduction:

Find the area of the complement of the difference of sets given by algebraic conditions:

This shows the set:

Use Implies to express set inclusion:

Properties & Relations  (2)

Truth table for binary Implies:

Implication of conditions in Boole functions:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)