SOLUTION: Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. p → (q ∨ p)

Algebra ->  Conjunction -> SOLUTION: Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. p → (q ∨ p)      Log On


   



Question 812001: Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
p → (q ∨ p)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
p → (q ∨ p)

The rule for a ∨ b "It is F only when a is F and b is F, otherwise it's T".
The rule for a → b "It is F only when a is T and b is F, otherwise it's T". 


p | q | q ∨ p | p → (q ∨ p) |
T | T |   T   |   T          |
T | F |   T   |   T          |
F | T |   T   |   T          |
F | F |   F   |   T          |

So p → (q ∨ p) is a tautology because the truth table contains only T's.

Edwin