A fresh recap on logical use of inclusive and exclusive or. Been thinking about this recently in association with other systems.

(That was a fun title to write!)

At the start of our discrete mathematics course we talk about symbolic logic. Students are often confused by the logical operator “OR.”

If p and q are statements then p OR q is true if either p is true or q is true or if both p and q are true. This is easily expressed in a truth table:

p | q | p OR q |

T | T | T |

T | F | T |

F | T | T |

F | F | F |

The reason this confuses students is that sometimes when we say “or” in everyday conversation we mean p is true or q is true, but p and q are not both true. (For example, “the door is open or the door is closed.”)

This brings to mind the logical operation *exclusive or*, “XOR” (the usual “or” is *inclusive or*). The truth table for XOR is…

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Use this tool (http://ckod.sourceforge.net/_/) of CKod (http://ckod.sourceforge.net/~/) for creating your “truth table”.