JAMIA 2023 — Mathematics PYQ

(i) $\{(1,(a,b)),(2,(b,c)),(3,(c,a)),(4,(a,b))\}$

• The first numbers are: 1, 2, 3, 4.

• Every first number is unique. Even though $1$ and $4$ both point to $(a,b)$, that is allowed.

• Result: It is a Function.

(ii) $\{(1,(a,b)),(2,(b,a)),(3,(c,a)),(1,(a,c))\}$

• The first numbers are: 1, 2, 3, 1.

• The number 1 appears twice. It tries to map to $(a,b)$ and $(a,c)$ at the same time.

• Result: Not a Function.

(iii) $\{(1,(a,b)),(2,(a,b)),(3,(a,b))\}$

• The first numbers are: 1, 2, 3.

• Every first number is unique. It is perfectly fine for different inputs to have the same output.

• Result: It is a Function.

(iv) $\{(1,(a,b)),(2,(b,c)),(1,(c,a))\}$

• The first numbers are: 1, 2, 1.

• The number 1 appears twice. It maps to $(a,b)$ in the first pair and $(c,a)$ in the last pair.

• Result: Not a Function.

Final Conclusion:

Only (i) and (iii) are functions.