**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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Find a countermodel for each of the following wffs: 3x p(x) → Vx p(x) Væ (p(x, f(x)) → p(x, y))

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

**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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