1. For each of the following statements find an equivalent statement in conjunctive normal form. Show...

1. For each of the following statements find an equivalent statement in conjunctive normal form. Show the proof and truth table.

a) ¬(A ∨ B)

b) ¬(A ∧ B)

c) A ∨ (B ∧ C)

2. Is the following implication true or false? And if false, give an example that shows that it is false.

If S1 ∈ S2 and S2 ∈ S3, then S1 ∈ S3

Expert Solution

~(A v B) => ~A ^ ~B (this is in cnf)

A    B    ~A    ~B    A v B   ~(A V B)    ~A ^ ~B

T    T     F    F       T       F           F

T    F     F    T       T       F           F
        
F    T     T    F       T       F           F   

F    F     T    T       F       T           T


Both ~(A v B) and ~A ^ ~B are same

~(A ^ B) = ~A v ~B (This is in cnf)

A    B    ~A    ~B    A ^ B   ~(A ^ B)    ~A V ~B

T    T     F    F       T       F          F

T    F     F    T       F       T          T

F    T     T    F       F       T          T

F    F     T    T       F       T          T


Both ~(A ^ B) and ~A V ~B are same

A v ( B ^ C) = (A V B) ^ (A V C) (this is cnf)

A   B   C   B ^ C    A V B     A V C  A v ( B ^ C)  (A V B) ^ (A V C)

T   T   T     T        T        T        T                T

T   T   F     F        T        T        T                T

T   F   T     F        T        T        T                T

T   F   F     F        T        T        T                T

F   T   T     T        T        T        T                T

F   T   F     F        T        F        F                F

F   F   T     F        F        T        F                F

F   F   F     F        F        F        F                F

Both A v ( B ^ C) and  (A V B) ^ (A V C) are same

S1 ∈ S2 and S2 ∈ S3, then S1 ∈ S3 this implicaiton is alway true

venereology answered 2 days ago

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1. For each of the following statements find an equivalent statement in conjunctive normal form. a) ¬(A ∨ B) b) ¬(A ∧ B) c) A ∨ (B ∧ C) 2. Is the following implication true or false? And if false, give an example that shows that it is false. ---> If S1 ∈ S2 and S2 ∈ S3, then S1 ∈ S3.

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Question

1. For each of the following statements find an equivalent statement in conjunctive normal form. Show...

Solutions

Expert Solution

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