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Question 669148: Given p is true, q is true, and r is false, find the truth value of the statement
~q → ( p V r )
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you're dealing with 2 basic truth tables here.
A or B is one of them.
A -> B is the other of them.
A or B truth table is as follows:
A B (A or B)
T T T
T F T
F T T
F F F
A -> B truth table is as follows:
A B (A -> B)
T T T
T F F
F T T
F F T
The bottom line on (A or B) is:
if A is true or B is true, then (A or B) is true.
The statement is true unless both of them are false, in which case the statement is false.
the bottom line of (A -> B) is:
If A is true and B is true, then (A -> B) is true.
If A is true and B is false,then (A -> B) is false.
If A is false, then (A -> B) is true regardless of whether B is true or false.
The only time the (A -> B) statement is false is if A is true and B is false. All other times the (A -> B) statement is true.
you are given the following:
p is true
q is true
r is false.
you need to find the truth statement of 3 statements.
they are:
~q
(p or r)
~q -> (p or r)
first find the truth value of ~q.
since q is given as true, then ~q has to be false.
you have:
~q is false
next find the truth value of (p or r)
since p is true and r is false, then (p or r) is true.
you have:
~q is false
(p or r) is true
now you need to find the truth value of ~q -> (p or r)
since ~q is false, then the statement ~q -> (p or r) has to be true regardless if (p or r) is true or false.
in this case you have ~q is false and (p or r) is true which makes ~q -> (p or r) F -> T which is true.
look at the truth table for A -> B to see the rules as they apply when A is false and B is true.
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