Question

let e be the set of even integers and let o be the set of odd integers. suppose that a computer is programmed to input a sequence of elements of e and output a sequence of elements of o according to some rule. you run a test of this program using 12,6,8,10,2 as input, and the computer outputs 81,9,25,49,1 . what rule does the computer appear to be using?

Answer 1

The rule the computer uses to convert even integers to odd integers seems to involve squaring the input and subtracting one, but the provided output sequence contains irregularities that do not fully match this rule.

Step-by-step explanation:

The student is asking about the apparent rule a computer uses to transform a sequence of even integers into a sequence of odd integers. After inputting the sequence of even integers 12, 6, 8, 10, and 2, the computer outputs the odd integers 81, 9, 25, 49, 1. Observing the pattern, the rule appears to be squaring the input number and subtracting one. For example, 12 squared is 144, minus one gives 143, but the output is 81, which is 9 squared (an earlier step in the squaring sequence). This suggests the computer is not only squaring and subtracting one but also seems to be taking the square root of a perfect square that is less than or equal to the squared even number before subtracting one to ensure an odd result. This requires further investigation as it does not directly explain the given outputs, and there may be a flaw in the observed outputs or an additional layer to the rule not immediately apparent from the given data.