Question 1172459
</pre>if p ^ ~ q is true<pre> 
^ is true when and only when there are true statements on both sides of it.
So p is true and ~q is also true.  

Therefore p is true and q is false.
</pre>and ~r🔛q is false then r must be ???.<pre>
I'm not sure what 🔛 means, but I think it's ↔, which is material equivalence.

Then ↔ is true when and only when the statements on both sides have the same truth value,
i.e., if and only if they are both true or they are both false.  

So we have so far that q is false, so ~r must have that same truth value.  So ~r is also 
false, which makes r true.

Edwin</pre>