I need some one to check my work please

Question

In exercise 51-60, write the statements in symbolic form.
p: The temperature is 90º.
q: The air conditioner is working.
r: The apartment is hot.
56. The temperature is not 90° if and only if the air conditioner is not working, or the apartment is not hot.

 

(∼p∨∼q)∨∼r

Answer 1

First, I’ll show you a couple of options for checking your work.

 

 

Option 1. Translate the symbols you wrote back into words.

 

~p (The temperature is not 90)

v (or)

~q (The air conditioner is not working)

v (or)

~r (The apartment is not hot)

 

You can see from this that yours symbols don’t match what the original statement.

 

Option 2: Use a truth table.

Since I can’t format a table in this forum, I can’t provide an example. I’m sure that you’ve seen far too many truth tables by now in your class :)

 

Now, let’s try working through the problem.

Take each statement and translate it into words.

~p (The temperature is not 90)

<-> (if and only if)

~q (the air condition is not working)

v (or)

~r (the apartment is not hot)

 

 

Which gives us: ~p<->(~qv~r)

 

 

I hope that helps. Good luck!