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In: Statistics and Probability

summary the principle 0f contradiction and how it applies

summary the principle 0f contradiction and how it applies

Solutions

Expert Solution

PRINCIPLE OF CONTRADICTION

  • the axiom or law of thought that a thing cannot "be and not be" at the same time, or a thing must either be or not be,or the same attribute can not at the same time be affirmed and and denied of the same subject; also called the lawof the excluded middle.
  • contradictory statements cannot both at the same time be true,

Example:-

  • the two propositions "A is B" and "A is not B" are mutually exclusive.
  • Butch is married to Barb but Barb is not married to Butch.---- is an implicit contradiction. It depends on the unstated but well known principle: if x is married to y, then y is married to x.  
  • A love B and A don't love B----is an explicit contradiction. You can't love someone and not love someone at the same time.

Application:-

for all propositions p, it is impossible for both p and not p to be true, or symbolically ∼(p · ∼p),

in which ∼ means “not” and · means “and”

orchestra answered 1 year ago
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