Question 325463
If p is true, but r is false, then *[Tex \LARGE p \wedge r] is false (both need to be true for it to be true).




So  *[Tex \LARGE \sim( p \wedge r)] is then true (it's the opposite of false).




Since *[Tex \LARGE \sim( p \wedge r)] is true, and we're dealing with an 'or' operation, we don't need to worry about the truth value of q or ~q because *[Tex \LARGE \sim( p \wedge r) \vee \sim q] is automatically true.




So on the flipside, *[Tex \LARGE \sim(\sim( p \wedge r) \vee \sim q)] is false.




So the entire expression is false.