Propositional Logic Example

Statements of Truth (Hypotheses)

  1. It is dark or the sun has set.
  2. If it is night then it is dark and the sun has set.
  3. If it is dark or the sun has set then it is night and it is dark.
Given the above truths we are required to prove that the sun has set.

Transforming Hypotheses to Logical Expressions

Let the following symbols represent the components of the statements as follows:
p - it is dark
r - it is night
q - the sun has set
By substituting these symbols in the hypotheses above we get the following logical expressions:
  1. p or q
  2. r -> p and q
  3. p or q -> r and p
We are required to prove q
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