Logical Reasoning
Develop deductive and inductive reasoning skills
Start with the basics and progress through 10 lessons. Each lesson builds on the previous one.
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10 questions, new mix each time (from 175)
In This Topic (10 lessons)
Introduction to Logical Reasoning
Learn the fundamentals of logical thinking and how to construct valid arguments in mathematics.
Deductive Reasoning
Learn how to use deductive reasoning to draw logical conclusions from given facts and premises.
If-Then Statements
Learn to write conditional statements in if-then form, find the hypothesis and conclusion, and decide when a conditional is false.
Converse and Inverse
Learn how to form the converse and the inverse of an if-then statement and why a true statement can have a false converse.
Contrapositive
Learn how to form the contrapositive of an if-then statement, why it always has the same truth value as the original, and how to use it to reason about numbers.
Pattern Recognition
Learn to spot the rule behind number and shape patterns, check it against every term, and predict what comes next.
Inductive Reasoning
Learn to make a conjecture from specific cases, test it with new ones, and break it with a counterexample.
Common Logical Fallacies
Learn to spot and fix the most common logical fallacies, from affirming the consequent to correlation vs causation, with math examples.
Syllogisms
Learn the four categorical statements, the parts of a syllogism, how to test validity with Venn diagrams, and how to chain if-then statements.
Logic Puzzles
Solve logic puzzles step by step with the grid method, elimination, case analysis, knights and knaves, ordering clues, number clues and river crossings.
Logical reasoning involves making valid conclusions from given information. Deductive reasoning moves from general to specific; inductive reasoning moves from specific to general. Both are essential for mathematical proofs and problem-solving.
What You'll Learn
- Distinguish deductive from inductive reasoning
- Identify valid and invalid arguments
- Recognize logical fallacies
- Apply reasoning to problem-solving
- Construct logical arguments
Frequently Asked Questions
What is deductive reasoning?
Starting with general premises to reach a specific conclusion. If premises are true, the conclusion must be true.
What is inductive reasoning?
Observing specific cases to make general conclusions. The conclusion is probable but not guaranteed.
What is a logical fallacy?
An error in reasoning that makes an argument invalid, such as circular reasoning or false dichotomies.