Introduction to Making Simple Deductions

Welcome! In this chapter, we are going to learn one of the most important skills in Thinking Skills: making simple deductions. Think of yourself as a detective. You are given a few pieces of information, and your job is to figure out what must be true based on those facts. In Paper 1 (Problem Solving), you won't just be guessing; you will be using logic to find the only possible answer.

Don't worry if logic puzzles sometimes feel a bit confusing. We will break them down step-by-step so you can approach any scenario with confidence!

What is a Deduction?

A deduction is a conclusion you reach by looking at the facts provided. Unlike a guess or an opinion, a logical deduction is certain. If the information you are given is true, then your deduction must also be true.

In the "Understanding and using information" section of your syllabus, simple deductions usually involve taking two or three pieces of information and linking them together to find a missing piece.

The "Must be True" Rule

When you are asked to make a deduction, always ask yourself: "Does this HAVE to be true, or is it just POSSIBLE?"

  • Possible: It could happen, but we aren't 100% sure. (This is NOT a deduction).
  • Necessary: Based on the facts, there is no other option. (This IS a deduction).

How to Make Deductions: A Step-by-Step Guide

To solve these problems in your exam, follow these simple steps:

Step 1: Identify the Facts

Read the scenario carefully and list the "rules" or data points given. Ignore any information that doesn't help you solve the specific question (this is called identifying relevant information, which we cover in another chapter).

Step 2: Find the Link

Look for a "bridge" between two facts. For example:

Fact 1: All students in the room are wearing blue shirts.
Fact 2: Sam is a student in the room.
The Link: Sam belongs to the group "students in the room."

Step 3: State the Conclusion

Combine the facts to find the result.
Deduction: Sam is wearing a blue shirt.

Quick Tip!

Always keep it simple. If you have to make five "maybe" jumps to get to an answer, you’ve probably gone too far. Simple deductions are usually just one or two logical steps away from the data.

Common Types of Simple Deductions

1. Numerical Deductions

These involve simple arithmetic. You might be given a total and some parts of that total, and you need to find the missing part.

Example: A box contains \( 20 \) pieces of fruit. \( 12 \) are apples and the rest are oranges.
Deduction: There must be \( 20 - 12 = 8 \) oranges.

2. Conditional Deductions (If/Then)

These follow a "rule." If a certain condition is met, then a specific result happens.

Example: If it rains, the football match is cancelled. It is currently raining.
Deduction: The match is cancelled.

3. Elimination

If you know there are only three possibilities (A, B, or C) and you prove that A and B are impossible, you have deduced that C must be the answer.

Key Terms to Remember

In the 2028 syllabus, you will see specific command words. Knowing these helps you understand what the examiner wants:

  • Identify: Pick out a specific piece of information.
  • Calculate: Work out a numerical answer using the facts.
  • State: Express the deduction clearly.
  • Explain: Show the steps of your reasoning (how you got from Fact A to Conclusion B).

Quick Review: In Paper 1, you must show your working! For exams in 2028 and beyond, the syllabus explicitly asks you to label your values with units and words (e.g., write "\( 5 \text{ apples} \)" instead of just "\( 5 \)").

Avoiding Common Mistakes

Even the best students can get tripped up by these common "logic traps":

1. Using Outside Knowledge: Only use the information given in the question. If the question says "All cats are green," then for that question, cats are green! Don't let real-world facts distract you from the logic of the scenario.

2. Reversing the Logic: Just because "If it rains, the match is cancelled" doesn't mean "If the match is cancelled, it must be raining." (Maybe the referee got sick instead!). This is a classic trap.

3. Confusing "All" with "Some": If the facts say some students like math, you cannot deduce that Sam (a student) likes math. You can only deduce something about Sam if the facts say all students like math.

Did You Know?

In Paper 1, even if you get the final answer wrong, you can often earn marks for the "correct steps" toward a solution. This is why showing your deductions clearly is so important!

Summary: Key Takeaways

  • Deductions are logical conclusions that must be true based on given facts.
  • Always look for the link between two pieces of information.
  • Use elimination if there are limited options.
  • Label your working with units and words to help the examiner follow your logic.
  • Don't assume anything that isn't written in the text.

Note: For more complex logic, see the chapter on "Make complex deductions." To understand how to use these facts in a bigger system, check out "Apply a simple model."