Given p is true, q is false, and r is false, find the truth value of the statement (q ^~r) ->~p.
Let's break it up to make it easier.
(q ^ ~r)
q is F.
~r is T.
Therefore, q ^ ~r is F.
~p is F.
Therefore, (q ^ ~r) --> ~p is T.
okay...that makes a little more sense...thanks Max!
You're welcome.
To find the truth value of the statement (q ^~r) ->~p, we need to evaluate each component of the statement individually and then combine them following the rules of propositional logic.
Let's break down the statement:
1. q is false
2. r is false
3. ~r is true (since ~ means negation, ~r is the opposite of r)
4. q ^ ~r is false (since ^ represents the logical AND operation, both q and ~r must be true for the statement to be true, but in this case, ~r is true and q is false)
5. p is true
Now, let's evaluate the statement (q ^ ~r) -> ~p:
1. (q ^ ~r) -> ~p can be rewritten as (~p v (q ^ ~r)) due to the logical equivalence of implication (p -> q is equivalent to ~p v q).
2. ~p is false (since p is true)
3. (q ^ ~r) is false (as stated earlier)
4. ~p v (q ^ ~r) is false v false, which is false.
Therefore, the truth value of the statement (q ^ ~r) -> ~p is false.