KB and S1 are two propositional logic statements, that are constructed using sym

Question

KB and S1 are two propositional logic statements, that are constructed using symbols A, B, C, and using various connectives. The above truth table shows, for each combination of values of A, B, C, whether KB and S1 are true or false.

Part a: Given the above information, does KB entail S1? Justify your answer.

Part b: Given the above information, does statement NOT(KB) entail statement NOT(S1)? Justify your answer.

S1 True True True TrueTrue TrueTrue False False True TruelFalse True True True TruelFalse False False True False True True FalseFalse False True False FalseFalse False False True FalseFalse False False False FalseFalse

Explanation / Answer

ANSWER :

Part a :

Condition for P entails Q : P entails Q whenever P is true, so is Q.We can say that
all models of P are also model of Q it means models(P) is a subset of model(Q).

Here in above given problem for every KB and S1 if KB is true, so is S1 is not true,
so KB does not entail S1.

Part b:
If KB does not entail S1 so NOT(KB) will also not entail NOT(S1)

NOT(KB) NOT(S1)
False False
True False
False False
True False
True True
True True
True True
True True

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