Question 569118: Given p is false, q is true, and r is true, find the truth value of the statement (p V ~q) ↔ ~r.
Show step by step work.
What in the world is truth value and how do I prove it?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A truth value is simply a value that can either be true or false.
Let's use the truth values given to evaluate the logical expression
(p V ~q) ↔ ~r ... Start with the given logical expression
(F V ~T) ↔ ~T ... Plug in p = F, q = T, r = T
(F V F) ↔ F ... Negate T to get F (since ~T = F)
F ↔ F ... Evaluate F v F to get F
T ... Since both sides are equal, the equivalence is true.
So the truth value of (p V ~q) ↔ ~r is T (or True) when p is false, q is true, and r is true
Notes:
1) p V q is only false when both p and q are false (otherwise it's true)
2) p ↔ q is only true if both p and q are of the same truth value (ie when both are either true at the same time or when both are false at the same time)
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