Propositional Logic Example
Statements of Truth (Hypotheses)
-
It is dark or the sun has set.
-
If it is night then it is dark
and the sun has set.
-
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:
- p or q
- r -> p and q
- p or q -> r and p
We are required to prove q
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