A conclusion must follow
If all objects in group A belong to group B, it does not follow that every object in B belongs to A. Check which direction the condition permits. A familiar or plausible statement is not automatically justified by the given premises.
Patterns need a complete check
A rule that explains one pair of items may fail elsewhere in a sequence or diagram. Test the proposed relationship against every relevant element. Distinguish information supplied by the task from assumptions added because they seem natural.
Justify each step
Write a problem’s conditions and explain which one supports each step. In the route task, check that all required locations are visited before comparing length. Keep difficulty and rules consistent when tracking time and errors across attempts.
Separate deduction from a guess
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Your result
Step-by-step worked example
What to prepare
Read three conditions about an imaginary card set. Decide which conclusions are guaranteed and which could be false.
Task sample
What to do, step by step
Separate the conditions from the questions: is A round, and must B be blue?
For A, apply the rule in its stated direction, from blue to round.
For B, construct a case that satisfies every condition while B is not blue, such as a red round card.
Write answers with reasons before opening the check. Do not replace unknown with no.
How to check your result
A must be round. B’s blue color does not follow: B could be blue or, for example, red and round. A correct explanation justifies A and supplies a valid counterexample to the claim about B’s color.
Your next attempt
Change colors and shapes while preserving the rule direction. Check each conclusion against the conditions and a doubtful reverse inference with a counterexample.
Examples in everyday tasks
Check the direction of a rule
All squares have four sides, so a square is four-sided. But a rectangle also has four sides, and the reverse claim that every four-sided figure is a square is false. Check the direction of the relationship instead of relying on familiar words or a plausible-sounding answer.
Identify incompatible instructions
One instruction permits sending a document only after a manager’s approval. Another requires sending before noon, while approval can only be obtained after 1 p.m. Under these conditions both cannot be satisfied. State the conflict explicitly and identify which condition needs clarification before constructing a solution.
Test a pattern throughout a series
For 2, 4, 8, 16, you propose doubling each number. Check every adjacent transition, not only the first pair. A short sequence can permit other continuations unless the rule is specified, so explain the pattern you selected and the evidence supporting it.
