$(Q\to R)\wedge (R\to Q)$ converting to sentence

33 Views Asked by At

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!