1. The most important idea in logic: Validity of an argument.
Logical Relations
The most important idea in logic:
Validity of an argument.

2. Logical Relations The most important idea in logic:
Validity of an argument.
Validity is a logical relation
between statements that make up an argument.

3. Logical Relations The most important idea in logic:
Validity of an argument.
Validity is a logical relation
between statements that make up an argument.
Namely that assuming premises are T
the conclusion has to be T.

4. Entailment Statement A entails statement B iff
It is not possible for A to be T and B to be F.

5. Entailment Statement A entails statement B iff
It is not possible for A to be T and B to be F.
The argument A | B has no counterexample.

6. Entailment Statement A entails statement B iff
It is not possible for A to be T and B to be F.
The argument A | B has no counterexample.
The argument A | B is valid.

7. Entailment Statement A entails statement B iff
It is not possible for A to be T and B to be F.
The argument A | B has no counterexample.
The argument A | B is valid.
Summary: Entailment is “one premise” validity.

8. Entailment More Generally:
we can speak of a group of statements entailing another:
A, B, C entails D
iff
A, B, C | D is a valid argument.

9. For more click here Testing Entailment To show A entails B ...
with a table: There is no A=T, B=F row.
with a proof: Given A, prove B.
with a tree: The tree for A, -B closes.
For more click here