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Exercises · Q7
Q.

The marks scored by five students in a business mathematics test are given below:

Roll No. (x)12345
Marks (y)4560457860

Write this information as a set of ordered pairs, and examine whether it represents a relation that is a function from the set of roll numbers to the set of marks. Justify your answer, and state the domain and range.

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✓ Free question

Ordered pairs. Reading the table row by row:

{(1,45),(2,60),(3,45),(4,78),(5,60)}\{(1,45), (2,60), (3,45), (4,78), (5,60)\}

Checking the function conditions. Every roll number 11 through 55 appears exactly once as a first co-ordinate, and each is paired with exactly one mark. It does not matter that the mark 4545 is repeated (for roll numbers 1 and 3) or that 6060 is repeated (for roll numbers 2 and 5) — the function condition only requires that each input (roll number) has a single output; it places no restriction on outputs repeating. So this relation is a function.

Domain = set of roll numbers actually used = {1,2,3,4,5}\{1, 2, 3, 4, 5\}.

Range = set of distinct marks actually obtained = {45,60,78}\{45, 60, 78\} (listed once each, even though 4545 and 6060 each occur twice).

Independent cross-check: counting the table directly — 5 roll numbers, 5 ordered pairs, no roll number missing and none repeated as a first element — confirms the function condition holds exactly as concluded.

✓Final answer

Yes, this is a function. Domain = {1, 2, 3, 4, 5}; Range = {45, 60, 78}.

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