SOLUTION: if p ^ ~ q is true and ~r🔛q is false then r must be

Question 1172459: if p ^ ~ q is true and ~r🔛q is false then r must be

Answer by Plocharczyk(17) (Show Source): You can put this solution on YOUR website!
if p ^ ~ q is true

 
^ 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.

and ~r🔛q is false then r must be ???.

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

RELATED QUESTIONS
If p is true, q is true, and r is false, then the truth value of ~[~(p^r) V ~q] is ?... (answered by jim_thompson5910)

P is True, q and r are False- find the truth value. a) (p ^ ~q) ^ r b)... (answered by Edwin McCravy)

Determine the truth value of the following statement if (a) p is true, q is false, and r (answered by solver91311)

if p is true, q is false, and r is true, find the truth value of the statement. (r... (answered by Theo)

if p is true, q is false, and r is true, find the truth value of the statement.(r → (answered by tinbar)

If P is true, Q is false and R is true. Find the true value of the statement.... (answered by solver91311)

if p is true and q is false and r is true what is the truth statement of the statement ~[ (answered by lynnlo)