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Q6E

Expert-verifiedFound in: Page 22

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

**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, ${\mathbf{u}}{\mathbf{\to}}{\mathbf{\left(}}{\mathbf{\right(}}{{\mathbf{b}}}_{{\mathbf{32}}}{\mathbf{\wedge}}{\mathbf{g}}{\mathbf{\wedge}}{\mathbf{r}}{\mathbf{\wedge}}{{\mathbf{h}}}_{{\mathbf{16}}}{\mathbf{)}}{\mathbf{\vee}}{\mathbf{(}}{{\mathbf{b}}}_{{\mathbf{64}}}{\mathbf{\wedge}}{{\mathbf{g}}}_{{\mathbf{2}}}{\mathbf{\wedge}}{{\mathbf{r}}}_{{\mathbf{2}}}{\mathbf{\wedge}}{{\mathbf{h}}}_{{\mathbf{32}}}{\mathbf{\left)}}{\mathbf{\right)}}$.

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

**"or"** is a logical sign. It can be depict as role="math" localid="1668083891892" ${\mathbf{\vee}}$.

**"and"** is a logical sign. It can be depict as ${\mathbf{\wedge}}$.

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

${\mathbf{u}}{\mathbf{\to}}{\mathbf{\left(}}{\mathbf{\right(}}{{\mathbf{b}}}_{{\mathbf{32}}}{\mathbf{\wedge}}{\mathbf{g}}{\mathbf{\wedge}}{\mathbf{r}}{\mathbf{\wedge}}{{\mathbf{h}}}_{{\mathbf{16}}}{\mathbf{)}}{\mathbf{\vee}}{\mathbf{(}}{{\mathbf{b}}}_{{\mathbf{64}}}{\mathbf{\wedge}}{{\mathbf{g}}}_{{\mathbf{2}}}{\mathbf{\wedge}}{{\mathbf{r}}}_{{\mathbf{2}}}{\mathbf{\wedge}}{{\mathbf{h}}}_{\mathbf{32}\mathbf{\left)}\mathbf{\right)}}$.

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