Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

You can upgrade your operating system only if you have a 32-bit processor running at 1 GHz or faster, at least 1 GB RAM, and 16 GB free hard disk space, or a 64- bit processor running at 2 GHz or faster, at least 2 GB RAM, and at least 32 GB free hard disk space. Express you answer in terms of u: “You can upgrade your operating system,” b32: “You have a 32-bit processor,” b64: “You have a 64-bit processor,” g1: “Your processor runs at 1 GHz or faster,” g2: “Your processor runs at 2 GHz or faster,” r1: “Your processor has at least 1 GB RAM,” r2: “Your processor has at least 2 GB RAM,” h16: “You have at least 16 GB free hard disk space,” and h32: “You have at least 32 GB free hard disk space.”

The logical proposition of the given statement is determined as, $u \to ((b_{32} \land g \land r \land h_{16}) \lor (b_{64} \land g_{2} \land r_{2} \land h_{32}))$ .

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TABLE OF CONTENTS :

TABLE OF CONTENTS

Introduction to the Concept

"If-then" is a logical sign. It can be depict as $\to$ .

"or" is a logical sign. It can be depict as role="math" localid="1668083891892" $\lor$ .

"and" is a logical sign. It can be depict as $\land$ .

Solution Explanation

The given statements are,

u: You can upgrade your operating system

b32: You have a 32-bit processor

b64: You have a 64-bit processor

g1: Your processor runs at 1 GHz or faster

g2: Your processor runs at 2 GHz or faster

r1: Your processor has at least 1 GB RAM

r2: Your processor has at least 2 GB RAM

h16: You have at least 16 GB free hard disk space

h32: You have at least 32 GB free hard disk space

The given statement's propositional logical expression is

$u \to ((b_{32} \land g \land r \land h_{16}) \lor (b_{64} \land g_{2} \land r_{2} \land h_{32))}$ .

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