Q only said to use Logic.

Never said what kind.

https://www.mathpages.com/home/kmath140/kmath140.htm

https://www.philosophybasics.com/branch_logic.html

Logical systems should have three things: consistency (which means that none of the theorems of the system contradict one another); soundness (which means that the system's rules of proof will never allow a false inference from a true premise); and completeness (which means that there are no true sentences in the system that cannot, at least in principle, be proved in the system).

Types of Logic

Logic in general can be divided into Formal Logic, Informal Logic and Symbolic Logic and Mathematical Logic:

Formal Logic:

Formal Logic is what we think of as traditional logic or philosophical logic, namely the study of inference with purely formal and explicit content (i.e. it can be expressed as a particular application of a wholly abstract rule), such as the rules of formal logic that have come down to us from Aristotle. (See the section on Deductive Logic below).

A formal system (also called a logical calculus) is used to derive one expression (conclusion) from one or more other expressions (premises). These premises may be axioms (a self-evident proposition, taken for granted) or theorems (derived using a fixed set of inference rules and axioms, without any additional assumptions).

Formalism is the philosophical theory that formal statements (logical or mathematical) have no intrinsic meaning but that its symbols (which are regarded as physical entities) exhibit a form that has useful applications.

Informal Logic is a recent discipline which studies natural language arguments, and attempts to develop a logic to assess, analyze and improve ordinary language (or "everyday") reasoning.

Symbolic Logic is the study of symbolic abstractions that capture the formal features of logical inference.

It is often divided into two sub-branches:

Predicate Logic: a system in which formulae contain quantifiable variables. (See the section on Predicate Logic below).

Propositional Logic (or Sentential Logic): a system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formulae to be established as theorems.

Mathematical Logic:

Both the application of the techniques of formal logic to mathematics and mathematical reasoning, and, conversely, the application of mathematical techniques to the representation and analysis of formal logic.

Logicism: perhaps the boldest attempt to apply logic to mathematics

Intuitionism: the doctrine which holds that logic and mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied.

Deductive reasoning concerns what follows necessarily from given premises (i.e. from a general premise to a particular one). However, it should be remembered that a false premise can possibly lead to a false conclusion.

Inductive logic is not concerned with validity or conclusiveness, but with the soundness of those inferences for which the evidence is not conclusive.

Modal Logic is any system of formal logic that attempts to deal with modalities (expressions associated with notions of possibility, probability and necessity).

Modalities are ways in which propositions can be true or false. Types of modality include:

Alethic Modalities: Includes possibility and necessity, as well as impossibility and contingency.

Propositional Logic (or Sentential Logic) is concerned only with sentential connectives and logical operators.

Predicate Logic allows sentences to be analyzed into subject and argument in several different ways, unlike Aristotelian syllogistic logic, where the forms that the relevant part of the involved judgments took must be specified and limited (see the section on Deductive Logic above).

Fallacies

A logical fallacy is any sort of mistake in reasoning or inference, or, essentially, anything that causes an argument to go wrong. There are two main categories of fallacy, Fallacies of Ambiguity and Contextual Fallacies:

Paradoxes

A paradox is a statement or sentiment that is seemingly contradictory or opposed to common sense and yet is perhaps true in fact.

It can be argued that there are four classes of paradoxes:

Veridical Paradoxes:

Falsidical Paradoxes

Antinomies

Dialetheias

(Paradoxes often result from self-reference)

Three doctrines which may be considered under the heading of Logic are:

Intuitionism

Logicism

Logical Positivism

So much Logic to choose from!

Which do you think is Q's favorite kind?