g10-01-03 · Core topics
Operations select different elements
Can union, intersection and difference use the same rule?
1 MIN · PREDICT ON PAPER
Choose A and B, predict which chips remain, then change only the operation.
Discuss or write first. No typed answer is required to continue.
Result = {3, 4, 5}
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
The decision for each element is respectively OR, AND, A-and-not-B, or not-A in U. Finite displayed cases suggest a conjecture; the justification below states why it holds under the stated conditions.
Conditions: U={1,…,8}; A={1,…,a}; B={b,…,8}. b=9 means B is empty.
Mathematical justification: For any x∈U, membership of the result is determined by its two truth values x∈A and x∈B. The displayed four regions partition U.
1 MIN · EXIT CHECK
If A={1,2}, B={2,3}, find A−B and A∩B.
Check after answering
A−B={1}; A∩B={2}.
Teacher guidance and extension
Before: Membership
Ask: Ask for one element distinguishing two operations.
Watch for: A−B need not equal B−A; a complement depends on its universe.
Challenge: Use element-by-element decisions to explain a De Morgan identity.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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