Set theory ek branch hai jiska main
focus hota hai objects (elements) ko
groups (sets) mein organize karne par.
Sets, distinct elements ka collection
hota hai. Set theory mein, hum
intersections, unions, subsets, and
complements jaise concepts se kaam
karte hain to study relationships
between sets.
Set theory mathematics mein ek
fundamental concept hai jo objects ko
organize karne aur compare karne ke
liye istemal hota hai.
1. Sets aur Elements: Set ek collection
hota hai jisme distinct elements hote
hain. For example, {1, 2, 3} ek set hai
jisme 1, 2, aur 3 elements hain.
2. Intersection aur Union: Intersection
mein do sets ka common elements
hota hain, jabki union mein dono sets
ke saare elements hote hain. Agar A =
{1, 2, 3} aur B = {3, 4, 5} hai, to A ∩ B =
{3} aur A ∪ B = {1, 2, 3, 4, 5}.
3. Subsets aur Supersets: Ek set jo
dusre set ke saare elements ko contain
karta hai, usko "superset" kehte hain.
Agar A = {1, 2} aur B = {1, 2, 3} hai, to A
⊆ B (A is a subset of B). Aur B ⊇ A (B is
a superset of A).
4. Complement: Ek set ka complement
uss universal set se hota hai jisme
woh
set exist karti hai. Agar U universal set
hai aur A = {1, 2, 3} hai, to A ka
complement A' ya A^c hoga, jo U mein
se {1, 2, 3} ke alawa ke elements hoga.
Set theory ka istemal algebra, geometry, logic, aur probability jaise areas mein hota hai. Yeh concepts mathematics ke foundation mein important role play karte hain aur higher-level concepts ko samajhne mein madad karte hain.
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