Need help understanding discrete mathematics logic

Question

I am having a heck of a time understanding Discrete Mathematics. I have tried this myself and put my answer below. If anyone could help me if my answer is incorrect could you please explain to me what I have done wrong? I really need to understand this.

Here is the question:

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

Here is my answer:

$u ↔ ((b32 ∧ r1 ∧ h16) ∨ (b64 ∧ g2 ∧ r2 ∧ h32) )$

Answer 1

As suggested by @GitGud in a comment, your only mistake is with the $\iff$.

Your logical statement is equivalent to:

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.

AND

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,
only if you can upgrade your operating system.

You can correct this error by changing the $\iff$ to $\implies$.