Bottom-Up Specification of Propositional Logic/Examples/Example 1
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Example of Bottom-Up Specification of Propositional Logic
The following is a WFF of propositional logic:
- $\paren {\paren {p \land q} \implies \paren {\lnot \paren {q \lor r} } }$
Proof
It is assumed that $p$, $q$ and $r$ are WFFs by $\mathbf W: \PP_0$.
By $\mathbf W: \text {OP}$:
By $\mathbf W: \neg$:
- $\paren {\lnot \paren {q \lor r} }$ is a WFF
By $\mathbf W: \text {OP}$:
- $\paren {\paren {p \land q} \implies \paren {\lnot \paren {q \lor r} } }$ is a WFF
$\blacksquare$
Sources
- 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.2$: Truth functions and truth tables: Example $1.3$