check the validity of the following argument: "if the rents of hotels in jammu are fixed or the prices of the commodities are reduced then the income of bussinessmen shall decrease. If the income of businessmen decrease then the farmer shall feel happy. The farmers never feel happy. Therefore the rents of the hotels are not fixed" .
2026-05-15 04:10:16.1778818216
Deduction from a sequence of statements
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Well, assume that the rents are fixed. What can you then deduce from the first setence? And, using that deduction, what does the second sentence then imply? Is that conclusion consistent with the assumption that the farmers aren't happy?
What you have here are implications $A \lor B \implies C$ and $C \implies D$. Which, by modus pones, implies $A \lor B \implies D$. Which is the same as $D \lor \lnot(A \lor B)$. If this propositions is to be true when $D$ is false, $\lnot (A \lor B)$ will have to be true. What does that tell you about $A$ and $B$?
(Here, $A$ means the rents are fixed, $B$ that the price of the commodities are reduced, $C$ that the income of businessman decreases, and $D$ that farmers are happy)