This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
 Documentation / Mathematica / Built-in Functions / Programming / Logical Operations  /
Implies

  • Implies[ p , q ] represents the logical implication .
  • Implies[ p , q ] is equivalent to ! p || q.
  • Implies[ p , q ] can be input in StandardForm and InputForm as pq. The character can be entered as => or \[Implies].
  • See the Mathematica book: Section 3.4.10.
  • See also: LogicalExpand, If.

    Further Examples

    The logical implication PQ is false only when P is true and Q is false.

    In[1]:=

    Out[1]=

    In[2]:=

    Out[2]=

    In[3]:=

    Out[3]=

    In[4]:=

    Out[4]=