A fair number of our reading assignments have contained logical symbols. Here are a few of these with translations. (Won't display properly unless you have the Lucida Sans Unicode font installed.)

symbol |
English equivalent |
interpretation |

& |
and |
P & Q is true if and only if P is true and Q is true |

⋁ |
or (inclusive) |
P ⋁ Q is true if and only if at least one of P and Q are true |

~ |
not |
~P is true if and only if P is false |

→ |
if . . . then |
P → Q is true if and only if either P is false
or Q is true (i.e. if P is true, so is Q; otherwise, if P is false, Q can be
either) |

∀x |
for all x |
∀x(x is a tree ⋁ ~(x is a tree) ) means that everything is either a tree or not a tree (literally: for all x, either x is a tree or x is not a tree) |

∃x |
there is an x such that |
∃x(x is a tree) says that there is a tree (at least one; could be more than one). Literally: there is an x such that x is a tree. |

Last update: January 28, 2002 |