Translate the given statement into propositional logic using the propositions provided.

You can upgrade your operating system only if you have a 32-bit processor running at I 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: t; “Your processor runs at 1 GHz or faster,” g2: “Your processor runs at 2GHz or faster,” rl: “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.”

Step 1:

Here we have to translate the given statement into propositional logic using the propositions provided.and we have to express our answer in terms of u,b32,b64,g1,g2,r1,r2,h16,h32

Step 2:

Given:u : “You can upgrade your operating system”

b32: “You have a 32-bit processor”

b64: “You have a 64-bit processor”

g1: t; “Your processor runs at 1 GHz or faster”

g2: “Your processor runs at 2GHz or faster”

rl: “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”

We need to translate the statement “You can upgrade your operating system only if you have a 32-bit processor running at I GHz or faster at least 1 GB RAM, and 16GB free hard disk space. or a 64-bit processor running at 2GHz or faster , at least 2 GB RAM, and at least 32 GB free hard disk space.” into propositional logic

Step 3:

Let us consider one by one statement first

You can upgrade your operating system only if

1.32-bit processor running at 1GHz that is .32-bit processor and running at 1GHz means

2. faster at least 1 GB RAM, and 16GB free hard disk space means

3.16 GB free hard disk space means b64

4. 64-bit processor running at 2GHz or faster means g2

5. least 32 GB free hard disk space is h32