SOLUTION: Math Construct a truth table for the following. Hint: you will need to use each of the columns! ((p V q) ∧ ~ q) → p p q

Algebra.Com
Question 1194343: Math
Construct a truth table for the following. Hint: you will need to use each of the columns!
((p V q) ∧ ~ q) → p
p q

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
((p V q) ∧ ~ q) → p

~ is negation, ~T gets an F and ~F gets a T
V is disjunction. F V F gets an F, everything else gets a T.
∧ is conjunction. T ∧ T gets a T, everything else gets an F.
→ is conditional. T → F gets an F, everything else gets a T. 

((p V q) ∧ ~ q) → p

 p | q | p V q | ~q | (p V q) ∧ ~ q || ((p V q) ∧ ~ q) → p |
 T | T |   T   |  F |         F     ||                 T   |
 T | F |   T   |  T |         T     ||                 T   |
 F | T |   T   |  F |         F     ||                 T   |
 F | F |   F   |  T |         F     ||                 T   |

Since it came out TTTT, all T's it is a tautology, always true.
 
Edwin

RELATED QUESTIONS

construct the truth table for each of the following statements.... (answered by MathLover1)
Construct a truth table for ( ~ p ^ q ) ---> ( ~ q v p ) (answered by CubeyThePenguin)
Construct the truth table for the following (i) p ^ (~p v q ) v (~q v p ) (ii) ~q if (answered by MathLover1)
Give a truth table that shows the Boolean value of each of the following Boolean... (answered by Edwin McCravy)
construct a truth table for the following: 1. ~p-> q 2.... (answered by jim_thompson5910)
Construct a truth table for (~p V ~q) -->... (answered by Fombitz)
Construct a truth table for (~p V... (answered by Fombitz)
Construct a truth table for (p V ~q) ↔ p (answered by jim_thompson5910)
construct a truth table for p^(~p v... (answered by Edwin McCravy)