3.3 Logical Reasoning & Word Puzzles

3.3 Logical Reasoning & Word Puzzles

Logical reasoning and verbal puzzles assess a candidate's capacity for deductive logic, pattern synthesis, and information processing. These skills are critical for military leadership, where decisions must be derived from incomplete, complex, or conflicting intelligence. This section covers categorical syllogisms, linear and circular ordering puzzles, multi-attribute logic matrices, verbal analogies, and classical deductive argument structures.

1. Syllogisms and Categorical Logic

A syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion. In the PMAEE, you must determine whether a conclusion logically follows from the given premises, regardless of real-world plausibility.

Categorical Propositions

• Universal Affirmative (All A are B): Every member of category A is inside category B. (A is a subset of B)
• Universal Negative (No A are B): There is zero overlap between category A and category B. (Intersection of A and B is empty)
• Particular Affirmative (Some A are B): At least one member of category A is also in category B. (Intersection of A and B is not empty)
• Particular Negative (Some A are not B): At least one member of category A is outside category B.

Rules of Syllogistic Validity

1. The Double Negative Fallacy: If both premises are negative (e.g., "No A are B" and "No B are C"), no logical conclusion can be drawn between A and C.
2. The Particular Limit: If one premise is particular (uses "some"), the conclusion must also be particular.
3. The Fallacy of the Undistributed Middle: The middle term (the term appearing in both premises but not the conclusion) must be "distributed" (referred to in its entirety) at least once. For example: "All cadets are disciplined. All athletes are disciplined." Here, "disciplined" is the middle term, but it is undistributed because neither premise covers the entire class of disciplined individuals. Therefore, you cannot conclude that "All cadets are athletes."

2. Verbal Logic and Ordering Puzzles

Ordering puzzles require you to arrange items or people based on comparative statements.

Solution Strategies

• Linear Ordering: Draw a straight line on your scratch paper and label the directions (e.g., North, South, or Left, Right). Place elements step-by-step as you resolve constraints.
• Identify Anchor Points: Look for definite statements first (e.g., "Cruz sits in the middle" or "Alab is at the far right"). Place these anchors first, then fit relative statements (e.g., "Bato is to the left of Cruz") around them.
• Kinship / Family Trees: When tracking relationships, draw a tree using symbols: use circles for females, squares for males, double lines for marriage, and single vertical lines for parent-child descent. Work backward from the final description (e.g., "my sister's mother" = "my mother").

3. Logic Matrices

Logic matrices, or grid puzzles, require matching multiple attributes (such as names, ranks, home provinces, and specializations) based on a series of clues.

Constructing and Using a Logic Grid

1. Draw a grid with names as rows and attributes as columns.
2. Mark cells with an "X" for confirmed mismatches and an "O" for confirmed matches.
3. Once an "O" is placed in a cell, fill the remaining cells in that row and column with "X" (since an attribute belongs to only one person).
4. Look for implicit clues. For example, "The sniper is from Baguio" means if you know Cadet Diaz is from Cebu, he cannot be the sniper.

4. Deductive Reasoning Rules and Fallacies

Deductive logic relies on valid structures. You must distinguish between valid reasoning and logical fallacies.

Deductive Logic Framework

Worked Scenario: Solving Linear Arrangements

Five cadets (Alab, Bato, Cruz, Diaz, and Esguerra) must be arranged in a line. You are told:

1. Cruz is in the middle (Position 3).
2. Alab is to the immediate right of Cruz (Position 4).
3. Bato is not at either end (cannot be Position 1 or 5).
4. Diaz is to the left of Bato.

By placing the absolute anchor first, Cruz goes to Position 3, and Alab goes to Position 4. Bato cannot be at 1 or 5, and since 3 and 4 are taken, Bato must be at Position 2. Since Diaz is to the left of Bato, Diaz must be at Position 1. This leaves Esguerra to occupy the remaining Position 5. The line from left to right is: Diaz, Bato, Cruz, Alab, Esguerra. Work systematically from the fixed boundaries inwards.

Common Fallacy Traps in Logic

• The Ad Hominem or Bias Trap: In verbal logic, you must evaluate the arguments based only on the premises provided. Do not let real-world facts or personal opinions influence your deduction. If a premise says "All fish can fly," you must treat it as absolute truth for the duration of that question.
• Incorrect Reversibility: Many test-takers assume that if "All A are B" is true, then "All B are A" is also true. This is a major logical trap. If all cadets are human, it does not mean all humans are cadets.