Consider the following statements : 1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z. 2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N. Which of the statements given above is/are correct?
Neither 1 nor 2
Neither statement is true. In statement 1, \((x,y)=(0,1)\) and \((0,2)\) give the same input 0 but outputs −1 and −2. In statement 2, \((1,6)\) and \((2,3)\) give the same input 6 but outputs 7 and 5. A function cannot assign two different outputs to one input.
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