Answered: Dean thinks that AB + A'B' simplifies…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Dean thinks that AB + A'B' simplifies to 1 by the Inverse law.

A. Show that Dean is wrong by fleshing out a truth table to find all rows in which AB + A'B' evaluates to 0, not 1. Circle these rows.

B. By part (a), A'B' is clearly not the inverse of AB. Using DeMorgan’s law, express the inverse of AB as a Boolean expression bexp_5b that is a sum of literals.

C. Extend the truth table from part (a) to add columns for bexp_5b and AB + bexp_5b. All entries in the column for AB + bexp_5b should have the value 1, showing that bexp_5b is indeed the inverse of AB.

Expert Solution

Step 1: Introduction

Given that:

AB+A'B'=1 by the inverse law:

To show that:

A) Dean is wrong by using truth table.

B) express the inverse of AB as a Boolean expression bexp_5b that is a sum of literals.

C) showing that bexp_5b is indeed the inverse of AB.

Concept:

To demonstrate that Dean is wrong and that $A B plus A apostrophe B apostrophe$ does not simplify to 1,

Let's create a truth table that evaluates the expression for all possible combinations of inputs $A$ and $B$ .

We will circle the rows where the expression evaluates to 0.

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