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Discrete Mathematics Homework: Proving a Logical Statement using Rules of Inference, Exercises of Mathematics

2nd Military Medical UniversityMathematics

A step-by-step solution to a discrete mathematics problem involving logical statements and the application of rules of inference. The problem includes given premises and requires the student to use universal instantiation, logical equivalence, de morgan's law, double negation law, commutative law, associative law, and resolution to prove a statement. Suitable for university students studying discrete mathematics or logic.

Typology: Exercises

2019/2020

Uploaded on 04/26/2020

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Discrete Mathematics Homework
1.4.37
1. ∀x(P(x)∨Q(x))/Premise
2. ∀x((¬P(x) ∧ Q(x))→R(x))/Premise
3. P(c)∨Q(c)/Universal instantiation from (1)
4. (¬P(c) ∧ Q(c))→R(c) /Universal instantiation from (2)
5. ¬(¬P(c) ∧ Q(c))∨R(c)/Logical equivalence from (4)
6. (¬¬P(c) ∨¬Q(c) )∨R(c)/De Morgan’s law from (5)
7. (P(c) ∨¬Q(c)) ∨R(c)/Double negation law from (6)
8. (¬Q(c) ∨P(c)) ∨R(c)/Commutative law from (7)
9. ¬Q(c) ∨(P(c)∨R(c))/Associative law from (8)
10. P(c) ∨(P(c)∨R(c))/Resolution from (3) and (9)
11. (P(c) ∨P(c)) ∨R(c)/ Associative law from (10)

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Discrete Mathematics Homework 1.4.

  1. ∀x(P(x)∨Q(x))/Premise
  2. ∀x((¬P(x) ∧ Q(x))→R(x))/Premise
  3. P(c)∨Q(c)/Universal instantiation from (1)
  4. (¬P(c) ∧ Q(c))→R(c) /Universal instantiation from (2)
  5. ¬(¬P(c) ∧ Q(c))∨R(c)/Logical equivalence from (4)
  6. (¬¬P(c) ∨¬Q(c) )∨R(c)/De Morgan’s law from (5)
  7. (P(c) ∨¬Q(c)) ∨R(c)/Double negation law from (6)
  8. (¬Q(c) ∨P(c)) ∨R(c)/Commutative law from (7)
  9. ¬Q(c) ∨(P(c)∨R(c))/Associative law from (8)
  10. P(c) ∨(P(c)∨R(c))/Resolution from (3) and (9)
  11. (P(c) ∨P(c)) ∨R(c)/ Associative law from (10)