Mathematics, 13.02.2020 20:46 PBWaffles4864
1. Consider the following hypotheses:
H1 : ∃x (p(x) ∧ q(x)) H2 : ∀x (q(x) → r(x))
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (p(x) ∧ r(x))
Clearly label the inference rules used at every step of your proof.
2. Consider the following hypotheses:
H1 : ∀x (¬C(x) → ¬A(x)) H2 : ∀x (A(x) → ∀y B(y)) H3 : ∃x A(x)
Use rules of inference to prove that the following conclusion follows from these hypotheses:
C : ∃x (B(x) ∧ C(x))
Clearly label the inference rules used at every step of your proof.
3. Consider the following predicate quantified formula:
∃x ∀y (P (x, y) ↔ ¬P (y, y))
Prove the unsatisfiability of this formula using rules of inference.
Answers: 1
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1. Consider the following hypotheses:
H1 : ∃x (p(x) ∧ q(x)) H2 : ∀x (q(x) → r(x))
...
H1 : ∃x (p(x) ∧ q(x)) H2 : ∀x (q(x) → r(x))
...
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