Answered: Prove the predictive logic statement is…

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

See similar textbooks

Related questions

Concept explainers

Question

Prove the predictive logic statement is valid: (∀ x)(P(x) → Q(a)) ∧ (∃ y)(P(y)) → Q(a)

Expert Solution

Step 1

Given,

The predictive logic statement: $(\forall x) (P (x) \to Q (a)) \land (\exists y) (P (y)) \to Q (a)$

The given predictive logic statement is valid if it is a tautology i.e., the truth values are always true regardless of the truth values of $P (x)$ and $Q (a)$ .

A truth table is a tool for evaluating the truth or falsity of a logical statement, given different combinations of truth values of its component propositions.

The truth table is as follows:

$P (x)$	$Q (a)$	$(\forall x) (P (x) \to Q (a))$	$(\exists y) (P (y))$	$(\forall x) (P (x) \to Q (a)) \land (\exists y) (P (y))$	$(\forall x) (P (x) \to Q (a)) \land (\exists y) (P (y)) \to Q (a)$
T	T	T	T	T	T
T	F	F	T	F	T
F	T	T	F	F	T
F	F	T	F	F	T

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions