How to specify the corresponding line of a truth table in a formula: $$p \to (\neg q \lor (q \to p))$$ $p$ evaluates to $F$ and $q$ evaluates to $T$.
I want to know the method followed to find this.
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I think you're asking, how do you evaluate the truth value of the formula, at those values of its variables?
You substitute those values for the variables (or constant symbols $\bot, \top$ for false and true respectively. Finally you evaluate the constant atomic subformulas and then the resulting constant atomic subformulas, and so on, iterating until you've reduced to a single (symbol for a) truth value, $\bot$ or $\top$.
Given the assignment $(p=\bot, q=\top)$, given that the formula is of the form $p\to \dotsc$, it's immediately obvious that the formula evaluates to $\top$, because $\bot\to\dotsc$ is always true. But we'll go through the exercise of substituting and reducing: $$\begin{align} p \to (\neg q \lor (q \to p))[\bot/p][\top/q] &= \bot \to (\neg \top \lor (\top \to \bot)) \\ &= \bot \to (\bot \lor (\top \to \bot)) \\ &= \bot \to (\bot \lor \bot) \\ &= \bot \to \bot \\ &= \top. \\ \end{align}$$
BrianO
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