SOLUTION: I am not to sure on this equation. Given p is true, and r is false, find the truth value of the statment ~q-->(p^~r)

Algebra ->  Conjunction -> SOLUTION: I am not to sure on this equation. Given p is true, and r is false, find the truth value of the statment ~q-->(p^~r)      Log On


   

Question 581882: I am not to sure on this equation. Given p is true, and r is false, find the truth value of the statment ~q-->(p^~r)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
~q-->(p^~r)

~q --> (T ^ ~F)

~q --> (T ^ T)

~q --> T

T

So regardless of the value of q, the entire expression is true. Why? Recall that p --> q is only false if both p is true and q is false. But in this case, q is true. So p --> q is true (and the value of p doesn't matter)