Question 669148
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:

<pre>
A   B   (A or B)
T   T      T
T   F      T
F   T      T
F   F      F
</pre>

A -> B truth table is as follows:

<pre>
A   B     (A -> B)
T   T         T
T   F         F
F   T         T
F   F         T
</pre>


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.