SOLUTION: Let p represent a true statement, while q and r represent false statements. Fing the truth value of the compound statement. a) (p^~q) ^ r b) ~(q v ~r)

Algebra ->  Conjunction -> SOLUTION: Let p represent a true statement, while q and r represent false statements. Fing the truth value of the compound statement. a) (p^~q) ^ r b) ~(q v ~r)      Log On


   

Question 88948: Let p represent a true statement, while q and r represent false statements. Fing the truth value of the compound statement.
a) (p^~q) ^ r
b) ~(q v ~r)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) 

(p^~q) ^ r


(T^~F) ^ F            Plug in the given truth values


(T^T) ^ F             Negate false (F) to get true (T)


(T) ^ F               Use a truth table to evaluate T^T to get T


F                     Use a truth table to evaluate T^F to get F



So (p^~q) ^ r is false


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b) 

 ~(q v ~r)


~(F v ~F)             Plug in the given truth values


~(F v T)              Negate false (F) to get true (T)


~(T)                  Use a truth table to evaluate F v T to get T


F                     Negate true (T) to get false (F)


So ~(q v ~r) is false