(Solved) : 1 25 Pts Brenda Anthony C Accused Interrogation Make Following Claims Brenda Says Anthony Q30869286 . . .
1. (25 pts) Brenda, Anthony, and C are accused of During theinterrogation they make the following claims:
Brenda says: “If Anthony is guilty then Charles is guiltytoo”.
Anthony says: “Brenda did it and Charles is innocent”.
Charles says: “I did not do it. One of the others, or maybe bothof them did it”
(a) Write a formula in propositional logic than represents theconjunction of the three above claims using the following atomicpropositions:
B: Brenda is guilty.
A: Anthony is guilty.
C: Charles is guilty
(b) Are the three above statements contradictory? Justify.
(c) Assuming that all of them are guilty, who lied during theinterrogation? Justify.
(d) Assuming that nobody lied, who is innocent and who isguilty? Justify.
2. (10 pts) Given the following formula F in:
(p ∨ q) → ((p ∨ q ∨ ¬r) ∧ (r ∨ p ∨ q))
Using only the equivalence transformations in PropositionalLogic, prove that the ¬F is a contradiction.
3. (35 pts) Convert (and simplify if possible) the followingsentences to Conjunctive Normal Form (CNF):
3.1. (P → Q) → ((Q → R) → (P → R))
3.2. (P → Q) ↔ (P → R)
3.3. (P ∧ Q) → (¬P ↔ Q)
3.4. ((P → Q) ∧ ¬Q) → ¬P
4.(30 pts) Check the following formulas for satisfiability usingthe Horn’s formula satisfiability test. If you verify that theformula is satisfiable, then present a model for it.
4.1.Q ∧ S ∧¬W∧(¬P∨¬Q∨V∨¬S)∧(S∨¬V)∧R
4.2.(¬A∨E) ∧¬B∧(¬C∨(A→B))∧A∧(¬E∨C∨¬D)∧(D∧(D∨F))
4.3. (P ∧ Q) → (¬P ↔ Q)
Expert Answer
Answer to 1 25 Pts Brenda Anthony C Accused Interrogation Make Following Claims Brenda Says Anthony Q30869286 . . .
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