Mathematics from zero

Logic and sets: free-recall review

Crux Free-recall prompts across the logic-and-sets unit: statements, the AND/OR/NOT rules, set membership, and union versus intersection. Answer first, then check.

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◷ 12 min

Recalling beats re-reading. For each prompt, say or write a full answer from memory first — then open the model answer and compare. The effort of pulling it back is what makes it stick.

Goal

Reconstruct the unit’s core ideas from memory: what makes a sentence a statement, how AND, OR, and NOT decide a truth value, what membership means for a set, and how union and intersection differ.

Recall before you leave

01
What makes a sentence a statement, and what does its truth value mean?
02
State the rule for AND and the rule for OR, and the one case where each one fails.
03
What does NOT do, and how would you evaluate NOT (a false statement)?
04
What is a set, and why does listing an element twice change nothing?
05
Explain the difference between the union and the intersection of two sets, with one example.
06
How do the two set operations mirror the two logical connectives from earlier in the unit?

Recap

If you could rebuild each answer from memory, you hold the unit’s spine: a statement carries a fixed true/false value; AND needs both true, OR needs at least one, NOT flips; a set records yes-or-no membership with no count of repeats; and the two set operations are just the two connectives applied to membership — union is ‘or’, intersection is ‘and’.

Continue the climb ↑Logic and sets: build a reasoning kit