Question 208804: Determine the truth value of the statement ~q <-> [~ r ~ (p ^ q)] when p is false, q is true, and r is true
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
There are 8 building blocks for ~q <-> [~r^(pvq)]
so that each successive one can be gotten by
doing negation, disjunction, conjunction, and
biconditional operations on one or two previous
building blocks, starting with the single letters:
~q <-> [~r^(pvq)]
1 p start with 1st single letter
2 q 2nd single letter
3 r 3rd single letter
4 ~r the negation of 3
5 (pvq) the disjunction of 1,2
6 [~r^(pvq)] the conjunction of 4,5
7 ~q the negation of 2
8 ~q <-> [~r^(pvq)] the biconditional of 6 and 7
Make a chart:
p q r ~r (pvq) [~r^(pvq)] ~q ~q <-> [~r^(pvq)]
| | | | | | | |
F T T F T F F T
So the truth value is T.
Edwin
|
|
|
