Ravi went to a shop and bought 3 pens and 2 notebooks for ₹85. If the cost of a pen is ₹x and a notebook is ₹y, the relation between x and y is 3x + 2y = 85. This relation from N to N is:

Ravi went to a shop and bought 3 pens and 2 notebooks for ₹85. If the cost of a pen is ₹x and a notebook is ₹y, the relation between x and y is 3x + 2y = 85. This relation from N to N is:

• A. a function
• B. not a function
• C. a bijection
• D. an equivalence relation

Answer: B) not a function

Explanation: For a given x, there could be multiple y satisfying the equation, or none. The relation is not a function because one x may correspond to more than one y (or no y). For example, x=5 gives 2y=70 → y=35; x=15 gives 2y=40 → y=20. But each x gives exactly one y actually: y = (85−3x)/2. Since it's a relation from N to N, it associates exactly one y to each x where 85−3x is even and positive. This defines a function from a subset of N. Since y = (85−3x)/2 gives a unique y for each x, it is a function. However, the domain is not all N, only those x where (85−3x) is a positive even integer. But the question says relation 'from N to N'. A function can have domain a proper subset. Actually, a relation R from A to B is a function if for every a ∈ A there is at most one b such that (a,b) ∈ R. Here, for each x ∈ N, there is at most one y. So it is a function (partial function). But the question might intend that not all x give a natural y, so it's not a function 'from N to N'? Usually 'function from A to B' requires domain = A. Since some x ∈ N do not yield y ∈ N, it's not a function from N to N. We go with 'not a function' because domain is not all of N. Yes, a function must be defined on the whole domain. So answer is 'not a function'.