Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. ~[(~q V p)^ ~r]
What do the ~ and V represent?
This does not look like a geometry question.
Write the statement in symbols using the p and q given. Then construct a truth table for the symbolic statement. p= The mouse is in the house. q= The cat is hungry
Either make a truth table from the combination of p,q, and r with the original expression, or simplify before doing same:
Expand using de Morgan's laws:
~[(~q ∧ p)^ ~r]
=~(~q ∧ p)∨ ~~r]
=(q ∧ ~p)∨ r
Can you make a truth table?
truth table don't understand it at all
To find the truth value of the compound statement ~[(~q V p)^ ~r], we need to evaluate the individual truth values of the statements ~q, p, and ~r and then combine them using logical operations.
Given:
q is false,
p is true,
r is false.
First, let's evaluate the individual statements:
~q signifies the negation of q, so ~q is true.
p is already given as true.
~r signifies the negation of r, so ~r is true.
Next, let's evaluate the compound statement using logical operations:
(~q V p) represents the disjunction (or) between ~q and p.
Since ~q is true and p is true, (~q V p) is true.
Now, we combine (~q V p) and ~r using the conjunction (and) operation:
((~q V p) ^ ~r) represents the conjunction of (~q V p) and ~r.
Since (~q V p) is true and ~r is true, ((~q V p) ^ ~r) is true.
Finally, we negate the result using the negation (~) operation:
~[((~q V p) ^ ~r)] represents the negation of ((~q V p) ^ ~r).
Since ((~q V p) ^ ~r) is true, ~[((~q V p) ^ ~r)] is false.
Therefore, the truth value of the compound statement ~[(~q V p)^ ~r] is false.