Relations / Function Types
Least You Need to Know: Injective, Surjective, and Bijective Functions
A function can fail by hitting two inputs with the same output, by missing outputs in the codomain, or by doing both.
جو کم از کم جاننا ضروری ہے
- Injective means distinct inputs give distinct outputs.
- Surjective means every element of the codomain is hit.
- Bijective means both injective and surjective.
- You test injective and surjective separately.
- The codomain matters for surjectivity.
اہم علامتیں
f:A→B
function from domain A to codomain B
injective
one-to-one
surjective
onto
مختصر حل شدہ مثال
- Let `f:{1,2,3}→{a,b,c}` with `f(1)=a`, `f(2)=b`, `f(3)=c`.\n- Every codomain value is hit and no two inputs share an output.\n- So `f` is bijective.
عام غلطیاں
- Students often test surjectivity against the image instead of the codomain.
- Students confuse 'not injective' with 'not a function'.
- A finite example can be injective but fail surjectivity if the codomain is larger.
اس قسم کے سوال کو کیسے پہچانیں
- The prompt names domain and codomain explicitly.
- The question asks whether values are repeated or missed.
- Function tables and small finite maps are ideal places to test injective versus surjective.
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