Sets — unique elements, set operations (union, intersection, difference)

1.2.25 · Coding › Introduction to Programming (Python)

Ek set hota kya hai

s = {3, 1, 2, 2, 3}      # duplicates collapse
print(s)                 # {1, 2, 3}  (order NOT guaranteed)
empty = set()            # {} is an empty DICT, not a set!

Uniqueness automatic kyun hoti hai — hashing idea

Chaar core operations

Maano $A$ aur $B$ sets hain. Har operation ek precise membership question ka jawab deta hai.

Figure — Sets — unique elements, set operations (union, intersection, difference)

Worked Examples

Worked example 1 — List dedup karna (80/20 use-case)

names = ["amy", "bob", "amy", "cara", "bob"]
unique = list(set(names))     # {'amy','bob','cara'} -> list

Ye step kyun? set(names) hashing se duplicates drop kar deta hai; list() mein wrap karna ek usable, indexable container return karta hai. Caveat: order lost ho jaata hai — agar first-seen order rakhna ho toh dict.fromkeys(names) use karo.

Worked example 2 — Numbers par saare chaar ops

A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
A | B   # {1,2,3,4,5,6}   union
A & B   # {3,4}           intersection
A - B   # {1,2}           difference (in A, not B)
B - A   # {5,6}           note it's different!
A ^ B   # {1,2,5,6}       symmetric difference

A ^ B = {1,2,5,6} kyun? Union {1..6} lo, shared {3,4} hata do. Jo bachta hai wo exactly ek set mein belong karta hai.

Worked example 3 — Do articles ke beech common tags

a1 = {"python", "data", "ml"}
a2 = {"ml", "stats", "data"}
shared = a1 & a2            # {'data','ml'}
only_a1 = a1 - a2           # {'python'}

Intersection kyun? "Dono mein common" literally AND ka English hai, jo exactly $\cap$ hai.

Worked example 4 — Forecast-then-Verify

Run karne se pehle predict karo:

X = {1, 1, 2, 3}
Y = {3, 4}
print(len(X))        # forecast: ___
print(X - Y)         # forecast: ___
print(2 in X)        # forecast: ___

Verify: 3 (dups collapse hokar {1,2,3} ban jaate hain) ; {1, 2} ; True.

Aur mistakes jo steel-man karni hain

Common mistake Set ke andar list daalna

{[1,2], 3}   # TypeError: unhashable type: 'list'

Sahi lagta hai: lists toh bas "values" hain. Sach: set ko hashable = immutable elements chahiye. Ek list change ho sakti hai, isliye uska hash bhi change ho jaata. Fix: tuple use karo: {(1,2), 3} ✅.

Key set algebra (derive karo, memorize mat karo)

Flashcards

Set ke elements ko distinct kya property banati hai?

Saare elements unique hote hain; duplicate inserts silently ignore ho jaate hain.

Empty set kaise banate hain (aur {} kyun nahi)?

set(); {} ek empty dictionary banata hai.

Set vs list mein x in s ki time complexity?

Set ≈

O (1)

(hash lookup); list ≈

O (n)

(linear scan).

Ek list set ka element kyun nahi ban sakti?

Set elements hashable/immutable hone chahiye; lists mutable hain, isliye unhashable. Tuple use karo.

A | B ka symbol aur matlab?

Union — elements A ya B mein.

A & B ka symbol aur matlab?

Intersection — elements A aur B mein.

A - B kya deta hai, aur kya ye symmetric hai?

A mein hai lekin B mein nahi waale elements; symmetric nahi (

A - B \neq = B - A

A ^ B kya deta hai?

Symmetric difference — elements jo exactly ek A ya B mein hain.

A.union(B) aur A.update(B) mein kya fark hai?

union ek naya set return karta hai; update A ko in place mutate karta hai.

List L dedup karne ka one-liner?

list(set(L)) (order preserved nahi hota).

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho do dibbon mein stickers hain. Ek set ek aisa dibba hai jisme ek jaisi do stickers nahi ho sakti — agar duplicate daalo, wo bas gayab ho jaati hai, ek hi bachti hai. Ab do dibbe leke:

Union = dono dibbe ek bade pile mein daal do (koi doubles nahi).
Intersection = sirf wahi stickers rakho jo dono dibbion mein hain.
Difference (Dibba A − Dibba B) = A ki woh stickers jo B ke paas nahi hain.
Symmetric difference = woh stickers jo sirf ek dibbe ke paas hain — "not-shared" waali. Aur dibba fast hai: "kya mere paas ye sticker pehle se hai?" check karne ke liye wo poora pile nahi dhundta — use exact jagah pata hoti hai dekhne ki.

Connections

Lists — ordered, indexed collections (sets order ke badle fast membership lete hain)
Dictionaries — key-value & why {} is a dict
Hashing and Hashable Types
Tuples — immutable sequences (valid set elements)
Big-O Notation & Time Complexity
Boolean Logic — AND, OR, XOR (set ops ke peeche ka algebra)