onstruct a Truth Table A. (p ^q) → p pap ^q→p B. p ^ ( q v r ) Û (p^q) v ( p ^r ) pgrp ^(q v r )ºp ^ q vp ^ r c. [ (p → q) ^ ( q→ r)] → (p → r ) pgrp → q^q → r→p → r
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![Construct a Truth Table
A(р^9) —р
pqp ^q→p
В.р^(qvr)0 (р^q)v(р^г)
pqrp ^(q vr)ºp^qvp^r
С. [ (р — ) ^ (9— г)] — (р —г)
pqrp → q^q → r→p → r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f33938-1262-472e-a491-6cc6ed412a8d%2F4d28768e-2a79-4926-9f31-71120e807d7e%2Fwxiyf49_processed.jpeg&w=3840&q=75)
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- Prove using truth table.There are two kinds of inhabitants in an island, one is knights, who always tell the truth, and the other, their opposites, knaves, who always lie. If you encounter three people P, Q, and R. What are P, Q, and R, if P says “Q and R are the same types”, Q says “R is knave”, and R says “P and R is the opposite types”? Show your work in detail and validate your answer in a mathematical way using truth table or proposition.2 not sure if I'm right on the 1st part, and don't understand how to get k=
- why don't we use the existential instantiation(∃x) instead of the universal because it says "A car" which means there exists one in the domain.If its TRUE: don't prove, but DO create an example that demonstrates the statement.IF FALSE: construct a counterexample.proof Lemma contrap : forall P Q : Prop, (P -> Q) -> (~Q -> ~P). use coq