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Question 483286: let p represent a true statement while q and r represent false statements. find the truth value of the compound statement
p^(qV~r)
true or false
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have three variables.
they are p, q, and r.
your compound statement is p ^ (q v ~r)
in english that would be:
p AND (q OR (not r))
here's your truth table:
p q r ~r (q v ~r) p ^ (q v ~r)
- - - -- -------- ------------
T T T F T T *****
T T F T T T *****
T F T F F F
T F F T T T *****
F T T F T F
F T F T T F
F F T F F F
F F F T T F
from this table, you can see that:
if p is true and (q or ~r) is true, then p ^ (q v ~r) is true.
in all other cases, p ^ (q v ~r) is false.
note that only one of q and ~r has to be true in order for the compound statement of (q v ~r) to be true.
if p is true, then the OR statement is true.
if ~q is true, then the OR statement is true.
The OR statement is only false if both p and q are false.
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