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Show that the following statement is a tautology using Truth Table

( p ^ q) --> p

I have some minor doubts in this seemingly simple question.

First a tautology is a statement which is always True, but while solving the question we get 1 False value, so how is still called a tautology?

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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.

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