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Let o be an arbitrary operation. Describe the operation o for the problem.
9 ο 3 = 12; 5 ο 1 = 6; 6 ο 4 = 10; 8 ο 2 = 10; ...

a. a ο b = a + b
b. a ο b = a x b / 2
c. a ο b = a + b + 1
d. a ο b = a - b
e. a ο b = 5a/2b

Sagot :

Answer:

a. a ο b = a + b

Step-by-step explanation:

Examining the given Equations

To identify whether "o" is an addition, subtraction, multiplication or division operation, seeing how the operation interacts and computes integers can give clues as to how "o" functions.

9 o 3 = 12

12 is the sum of the terms 9 and 3.

5 o 1 = 6

6 is the sum of the terms 5 and 1.

6 o 4 = 10

10 is the sum of 6 and 4.

8 o 2 = 10

10 is also the sum of 8 and 2.

Seeing that the "o" operations computes the sum of the given integers, "o" must be the addition operation or A that swaps the "o" for a "+".

The operation defined by a. a ο b = a + b satisfies all given conditions

We need to find the correct operation that satisfies the following:
1. 9 ο 3 = 12
2. 5 ο 1 = 6
3. 6 ο 4 = 10
4. 8 ο 2 = 10

We can test each of the provided options:

  1. a ο b = a + b
    9 + 3 = 12 (correct)
    5 + 1 = 6 (correct)
    6 + 4 = 10 (correct)
    8 + 2 = 10 (correct)
  2. b. a ο b = a x b / 2
    9 x 3 / 2 = 13.5 (incorrect)
    5 x 1 / 2 = 2.5 (incorrect)
    6 x 4 / 2 = 12 (incorrect)
    8 x 2 / 2 = 8 (incorrect)
  3. c. a ο b = a + b + 1
    9 + 3 + 1 = 13 (incorrect)
    5 + 1 + 1 = 7 (incorrect)
    6 + 4 + 1 = 11 (incorrect)
    8 + 2 + 1 = 11 (incorrect)
  4. d. a ο b = a - b
    9 - 3 = 6 (incorrect)
    5 - 1 = 4 (incorrect)
    6 - 4 = 2 (incorrect)
    8 - 2 = 6 (incorrect)
  5. e. a ο b = 5a / 2b
    5 x 9 / 2 x 3 = 7.5 (incorrect)
    5 x 5 / 2 x 1 = 12.5 (incorrect)
    5 x 6 / 2 x 4 = 7.5 (incorrect)
    5 x 8 / 2 x 2 = 10 (correct)

From these evaluations, we see that a ο b = a + b fits all given conditions. Therefore, the operation is defined as a ο b = a + b.

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