Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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**Find a countermodel for each of the following wffs:**

1. \(\exists x \, p(x) \rightarrow \forall x \, p(x)\)

2. \(\forall x \, (p(x, f(x)) \rightarrow p(x, y))\)

In this context, "wffs" stands for "well-formed formulas," which are logical expressions constructed using the syntax rules of a formal language. A countermodel is an interpretation under which the given formula is false. The task involves finding interpretations or examples where these logical formulas do not hold universally.
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Transcribed Image Text:**Find a countermodel for each of the following wffs:** 1. \(\exists x \, p(x) \rightarrow \forall x \, p(x)\) 2. \(\forall x \, (p(x, f(x)) \rightarrow p(x, y))\) In this context, "wffs" stands for "well-formed formulas," which are logical expressions constructed using the syntax rules of a formal language. A countermodel is an interpretation under which the given formula is false. The task involves finding interpretations or examples where these logical formulas do not hold universally.
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