Set Cardinality: |A ∪ B|
Sets · Class XI
Pick sizes of A, B and their intersection , watch how union and difference cardinalities update.
- |A ∪ B|30
- |A − B|15
- |B − A|10
- Symmetric Diff |A Δ B|25
Formulas in this lab
- |A ∪ B|
- |A − B|
- |B − A|
- Symmetric Diff |A Δ B|
Frequently asked questions
▶What is the inclusion-exclusion formula $|A\cup B| = |A| + |B| - |A\cap B|$?
When you add $|A|$ and $|B|$, the elements common to both get counted twice, so you subtract $|A\cap B|$ once to fix the over-count. If $|A| = 20$, $|B| = 15$ and $|A\cap B| = 5$, then $|A\cup B| = 30$. This single identity powers most Class XI set problems.
▶How do I use the set cardinality lab?
Slide $|A|$, $|B|$ and $|A\cap B|$. The lab instantly returns $|A\cup B|$, $|A-B|$, $|B-A|$ and the symmetric difference $|A\,\Delta\,B| = |A|+|B|-2|A\cap B|$. Keep $|A\cap B|\le\min(|A|,|B|)$ for a valid Venn diagram.
▶Why do students lose marks on $|A\cup B\cup C|$ in board exams?
Most slip on the three-set version: $|A\cup B\cup C| = |A|+|B|+|C|-|A\cap B|-|B\cap C|-|A\cap C|+|A\cap B\cap C|$. They forget the $+|A\cap B\cap C|$ at the end. Master the two-set case in this lab first, then the three-set pattern follows naturally.
▶Where is inclusion-exclusion used in real life?
Coaching surveys ask things like: 60 students take Physics, 50 take Chemistry, 30 take both — how many take at least one? Answer: $60+50-30 = 80$. The same logic prices insurance policies, sizes mailing lists and counts JEE aspirants across overlapping streams.