patternMinor
Is it a tautology or not? According to my truth table its not
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tautologyaccordingitstruthnottable
Problem
If $\bigr((q\leftrightarrow p)\leftrightarrow s\bigl)$ is a tautology and $p\rightarrow s$ is contingent, does it follow that $q\rightarrow s$ is contingent?
Since I can't show $\bigr((q\leftrightarrow p)\leftrightarrow s\bigl)$ is a tautology, I'm unsure how to proceed.
Since I can't show $\bigr((q\leftrightarrow p)\leftrightarrow s\bigl)$ is a tautology, I'm unsure how to proceed.
Solution
The question is not phrased clearly. Perhaps the question can be rephrased as follows: Let $p,q$ and $s$ be propositions whose truth values belong to some subset $A \subseteq \{T,F\}^3$. Suppose $A$ is such that $(q \leftrightarrow p) \leftrightarrow s$ evaluates to true for each assignment from $A$ and $p \rightarrow s$ can take both possible truth values over assignments from $A$. Can $q \rightarrow s$ take both possible truth values over assignments from $A$?
But there are many $A$'s which satisfy the given two conditions, and different $A$'s will give different answers- it can be a contingency, or it can be tautology.
But there are many $A$'s which satisfy the given two conditions, and different $A$'s will give different answers- it can be a contingency, or it can be tautology.
Context
StackExchange Computer Science Q#109845, answer score: 3
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