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Sagot :
Answer:
True
Explanation:
To find the true value of the statement, we will use the following table:
p ~p
True False
~p represents the negation p, So if p is True the negation of p is False.
In the same way, ~q is true because q is False, so its negation is true.
q ~q
False True
Now, we need to find the value of (~p^~q), where the symbol ^ represents the conjunction 'and'. So, (~p^~q) is:
~p ~q (~p^~q)
False True False
Because a statement with the conjunction 'and' is true only if both statements are true. Since ~p is False, ~p^~q is also false.
Then, we can find the value of (~p^~q)v~p), where the symbol v represents the conjunction 'or'. So, (~p^~q)v~p is:
(~p^~q) ~p (~p^~q)v~p
False False False
Because a statement with the conjunction 'or' is False only if both statements are false. Since (~p^~q) is false and ~p is false, then [(~p^~q)v~p] is also False.
Finally, we can find the value of the complete statement ~[(~p^~q)v~p)] as:
(~p^~q)v~p) ~[(~p^~q)v~p)]
False True
Because the negation of a False Statement is True
Therefore, the truth value of the compound statement is True
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