Inclusive “or” is true when P is true, Q is true, or both P and Q are true.
Duration of the online course: 4 hours and 48 minutes
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Build sharp logic skills with a free online course: master conditionals, truth tables, and clear reasoning for school, work, and tests—plus practice.
Logical reasoning is a practical skill that improves how you think, argue, and solve problems. This free online course helps you turn everyday statements into clear, testable forms so you can spot errors, avoid ambiguity, and make decisions with confidence. Whether you are strengthening school foundations, preparing for exams, or aiming to communicate more precisely at work, you will learn to analyze ideas the way mathematicians, programmers, scientists, and strong critical thinkers do.
You will start by learning how to recognize simple statements and represent them in a compact way, which makes complex arguments easier to handle. From there, you will build powerful tools step by step: negation, disjunction and conjunction, and the core relationships behind if-then reasoning and if and only if statements. Along the way you will see how small wording differences change meaning, why certain expressions can become ambiguous, and how symbolic notation helps keep your thinking consistent and precise.
A major focus is understanding truth conditions. You will use truth tables to evaluate whether statements hold under different scenarios, practice analyzing combinations, and develop intuition for patterns that repeatedly appear in logical problems. You will also learn why some implications are considered true even when their starting condition is false, a concept that often surprises beginners but becomes clear once you work with the formal definitions.
As you progress, you will learn efficient transformations that let you simplify and reframe expressions without recalculating everything. You will work with exclusive or, double negation, material implication, contraposition, and DeMorgan’s laws, all of which help you rewrite statements into equivalent forms that are easier to check and use. By the end, you will be able to translate complicated sentences into logic, verify reasoning reliably, and apply these skills to school subjects, structured writing, and analytical tasks in many professions.
4 hours and 48 minutes of online video course
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
What does the inclusive “or” mean in propositional logic?
Inclusive “or” is true when P is true, Q is true, or both P and Q are true.
Why is an if-then statement true when its antecedent is false?
In material implication, “if P then Q” is false only when P is true and Q is false; otherwise it is true.
How does contraposition simplify a conditional statement?
A conditional “if P, then Q” is logically equivalent to its contrapositive: “if not Q, then not P.”
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Course comments: Logic Reasoning 101
muhammad nadeem khan
good
muhammad nadeem khan
it is great and skillful