Truth Table Approach:
P |
Q |
P^Q |
P^Q-->P |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
We can conclude from the truth table that this is indeed a Tautology,
To explain this in a bit more simple manner, lets take a look at the definition of A->B ,this states that "When A is true then B should be true" .This states nothing about what happens when A is false. Therefore whenever A is false the proposition is automatically true.
so in the first three cases as P^Q is false therefore P^Q->P is true.
in the last case as P^Q is true and P is true therefore the proposition is true.
As this proposition is true for all values hence this is a tautology.