"The Air Conditioner Is On; However, the Fan Is Not $\rightarrow$

Multiple Choice

"The air conditioner is on; however, the fan is not. So, it's cooler because if the air conditioner were on, it would be cooler." Choose the best symbolization of the statement and evaluate its validity.

A) a & ~ f, a $\rightarrow$ c, c; this argument is valid
B) a & ~ f, c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 a $\rightarrow$ c; this argument is invalid
C) None of the answers are correct
D) a & ~ f, a $\rightarrow$ c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 c; this argument is invalid
E) a & ~ f, c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 a $\rightarrow$ c; this argument is valid