L3
If-Then Logic
条件推理
Logic / 逻辑Grades G4 - G7
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Statements with 'if...then'
- 2Questions about what can be concluded
- 3Deductive reasoning problems
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What It Really Tests
The core mathematical idea behind this structure:
From 'If P then Q', we can deduce certain conclusions but not others.
从'如果P则Q'，我们可以推出某些结论但不是其他结论。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Affirming the consequent (Q doesn't prove P)
- ⚠Denying the antecedent (not P doesn't prove not Q)
- ⚠Confusing necessary with sufficient conditions
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Your First Step
How to begin thinking about problems with this structure:
Valid: If P then Q, and P is true, so Q is true. Also: If P then Q, and Q is false, so P is false. Invalid: can't conclude anything from Q alone.
有效：如果P则Q，且P为真，所以Q为真。还有：如果P则Q，且Q为假，所以P为假。无效：仅从Q无法得出结论。
Related Structures
These structures share similar patterns or thinking approaches: