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Suppose we assume the logic has just 5 statement letters (i.e. Boolean variables): A, B, C,...

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Advance Math

Suppose we assume the logic has just 5 statement letters (i.e.Boolean variables): A, B, C, D, and E.

E1. Show a model that is a counterexample to (A ^ B) |= (B--> (not C))?

E2. Expand the definition of entailment in the following twostatements, explaining without using \"entails\" what they mean:

a. P |= (Q v R)

b. either (P |= Q) or (P |= R) or both Here, P, Q, and R arearbitrary formulas.

E3. Prove that 2a and 2b are not necessarily the same by findingformulas P, Q, and R for which one is true and the other isfalse.

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