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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Boolean Computation >

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Built-in Mathematica Symbol

Implies ()

Implies[p, q]
represents the logical implication

Implies[p, q] can be input in StandardForm and InputForm as . The character can be entered as Esc => Esc or \[Implies].

Enter using Esc => Esc:

Certain arguments automatically simplify:

Expand in terms of And, Or and Not:

Do symbolic simplification:

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:

Truth table for Implies:

Implication of conditions in Boole functions: