Conditional Logic Test

How conditional rules work

A rule such as A → B means: if A is true, B must also be true. It does not mean that A must be true whenever B is true.

The logically equivalent contrapositive is not B → not A. Reversing the rule to B → A, or negating both sides to not A → not B, is not valid.

The five question types

• Implication: apply a direct if–then rule to a known fact.
• Contraposition: reason backward from a result that did not happen.
• Rule Chains: connect two or more rules before choosing the forced conclusion.
• Conditions: translate necessary and sufficient language into symbols, or find the case that satisfies every rule at once.
• Verbal Conditionals: everyday if–then statements where sometimes none of the listed statements must follow from the known fact. In these rounds, “Statement B holds” means Statement B is true, while “Statement B fails” means it is false.

Two ways the abstract questions are asked

Implication, Contraposition, and Rule Chains alternate between two formats. Some ask which of four statements must be true. Others show a single statement and ask whether it must be true, could be true, or cannot be true.

The second format is the harder one and the more useful one. A statement that could be true is consistent with the rules but is not forced by them, so treating it as proven is an error. A statement that cannot be true is ruled out by the rules. Sorting a claim into the right one of those three boxes is the skill most aptitude and admissions tests are actually measuring.

How difficulty changes the Verbal rounds

Easy gives one rule per statement, so a single pass down the rule list settles the answer. Medium adds a second rule to every statement, so both the forward reading and the contrapositive reading have to be checked, and most of the rules turn out to be irrelevant. Hard returns to one rule per statement but routes every chain through an intermediate statement, so reaching a conclusion takes two linked steps rather than one.

Necessary and sufficient conditions

If A is sufficient for B, then A → B. If A is necessary for B, then B → A. “A if and only if B” means both directions hold.

When none of the listed statements must follow

Two patterns look convincing and may fail to prove any listed answer. Knowing a result happened does not prove a particular condition happened, because something else may have caused it. Knowing a condition did not happen also does not establish the result. In those cases, choose “None of the listed statements must follow” only when none of the three listed statements is forced by the rules and known fact.

Scoring

Your score is based on accuracy. Average response time and the five skill scores are shown separately, so you can see which pattern is costing you points. Mixed difficulty distributes Easy, Medium, and Hard questions across the session.

Controls

Click an answer, or use the number keys for the options shown. In Practice mode the app explains each answer and then waits for you to continue. Active-time measurement pauses when the tab is hidden or a dialog is open. Advanced Settings let you drill a single skill.