Kenneth Rosen Edition 7 Exercise 1.2 Question 6 (Page No. 22)

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,” 
b$_{32}$: “You have a 32-bit processor,”
b$_{64}$:“You have a 64-bit processor,” g1: “Your processor runs at 1 GHz or faster,”
g$_2$: “Your processor runs at 2 GHz or faster,”
r$_1$: “Your processor has at least 1 GB RAM,”
r$_2$: “Your processor has at least 2 GB RAM,”
h$_{16}$: “You have at least 16 GB free hard disk space,”
and h$_{32}$: “You have at least 32 GB free hard disk space.”

Answer 1

u $\rightarrow $((b32 ⋀ g1 ⋀ r1 ⋀ h16) ⋁ (b64 ⋀ g2 ⋀ r2 ⋀ h32))

because p only if q means (p $\rightarrow$ q).

Answer 2

u ⟵ ((b₃₂ ⋀ g₁ ⋀ r₁ ⋀ h₁₆) ⋁ (b₆₄ ⋀ g₂ ⋀ r₂ ⋀ h₃₂))

Comments

Isn't the answer should be u -> ((b₃₂ ⋀ g₁ ⋀ r₁ ⋀ h₁₆) ⋁ (b₆₄ ⋀ g₂ ⋀ r₂ ⋀ h₃₂)) as the conditional statement in the answer by @srestha will be true when necessary condition is not satisfied and system can be upgraded..