NCERT Class 12 · Ch 1 Exercise 1.2 · Q6
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.2 Question 6
Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}. Show that f:A→B is one-one.
💡 Concept Hints
- Compare the outputs attached to the three domain elements.
- Separate the one-one and onto claims. For onto, ensure each inverse candidate lies in the allowed domain.
✅ Step-by-Step Solution
Final Answer: f is injective.
- The distinct domain inputs 1,2,3 have outputs 4,5,6 respectively.
- These three outputs are pairwise distinct. Thus f(a)=f(b) forces a=b for a,b∈A.
- Therefore f is one-one. The unused codomain element 7 concerns onto, not injectivity.
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