# NEGATION APPLIED TO A CONJUNCTION

## Let P and Q be sentences which are true or false, but neither of them
is both. "Not(P and Q)" means the same thing as "(not(P)) or
(not(Q))".

The Negation of a Conjunction is equivalent to an Alternation
of the Negations of the conjuncts
P |
Q |
P and Q |
not(P and Q) |
not(P) |
not(Q) |
(not(P)) or (not(Q)) |

T |
T |
T |
F |
F |
F |
F |

T |
F |
F |
T |
F |
T |
T |

F |
T |
F |
T |
T |
F |
T |

F |
F |
F |
T |
T |
T |
T |

Some people understand this principle as follows. They know that "P and
Q" is true only when both P and Q are true. For it to be false, P is false
or Q is false (possibly both are false, which fits our understanding of
"or"). P being false makes "not(P)" true; Q being false makes "not(Q)"
true. So, "not(P)" is true or "not(Q)" is true (possibly both are true).
This is exactly what is meant by "(not(P)) or (not(Q))".

The truth table to the right is a different approach to the same
principle. Note that columns 4 and 7 have identical truth values.

This is one of the famous DeMorgan transformations developed by
Augustus Demorgan.