$(Q\to R)\wedge (R\to Q)$ converting to sentence Well, I am following this video lecture (MOOC) and I came across this quiz where I have to convert $(Q\to R)\wedge (R\to Q)$  to sentence.

$Q$: "I will go to town"

$R$: "I have time"

My answer to $(Q\to R)\wedge (R\to Q)$  is 

"I will go to town ONLY IF I have time AND I have time ONLY IF I will go to town".

Whereas, the professor teaching in video gave following answer:

"I will go to town ONLY IF I have time AND IF I have time I will go to town".

I don't get the answer given by professor because it changes the meaning of sentence after 'AND'.

NOTE: Further professor explain that this can be converted to equivalent "If and Only If", but my concern is not on equivalence. I understand that part.

Thank you in Advance!
Your answer and the professor's answer are both correct.  Other ways to say $p$ implies $q$ are: "if $p$ then $q$" and "$p$ only if $q$".  You can replace "only if" by "implies".  

Thus, "I have time ONLY IF I will go to town" and "IF I have time I will go to town" both say the same thing - "I have time implies I will go to town".