SOLUTION: If P is true, Q is false and R is true. Find the true value of the statement. ~[P➡(Q^R)]

Algebra ->  Expressions-with-variables -> SOLUTION: If P is true, Q is false and R is true. Find the true value of the statement. ~[P➡(Q^R)]      Log On


   

Question 984118: If P is true, Q is false and R is true. Find the true value of the statement. ~[P➡(Q^R)]
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


A conditional is false whenever the antecedent is true and the consequent is nevertheless false. P, the antecedent, is true, but since Q is false, Q and R is false, the consequent is false and therefore the conditional is false.

The entire truth table for your statement is:
  P   Q   R   Q&R   P->(Q&R)
  T   T   T    T       T
  T   T   F    F       F
* T   F   T    F       F
  T   F   F    F       F
  F   T   T    T       T
  F   T   F    F       T
  F   F   T    F       T
  F   F   F    F       T

The line with the asterisk is the given situation.
John

My calculator said it, I believe it, that settles it