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Question 263274: 7. Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
[(~q V r) Λ~p]
(Points :3)
True
False
i picked true
Answer by mducky2(62)   (Show Source):
You can put this solution on YOUR website! Let's put this into words and simplify it. We know that V = or, ~ = not, and Λ = and.
[(~q V r) Λ~p]
[((not q) or r) and not p]
Now let's plug in true (T) or false (F) for all the letters. According to the problem, p = T, q = F, and r = F.
[((not q) or r) and not p]
[((not F) or F) and not T]
We can simplify this down by replacing "not F" with "T" and "not T" with "F".
[((not F) or F) and not T]
[(T or F) and F]
For "or" equations, the equation is true if either one is true. Since one is true, it becomes T.
[(T or F) and F]
[T and F]
For "and" equations, the equation is true only if both are true. Since one is not true, it becomes F.
[F]
The answer is false.
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