hello can you help me answer this? im really not good in math

this usbject is MATHEMATICS IN MODERN WOLRD.. please help. please also show some solutions on how you come up with tha nswer please help me im really having a hard time..

31. If (2a + b, a - b) = (8, 3), what should be the values of a and b?

a. a=11/3 and b= 2/3 c. a = 2/3 and b = 11/3

b. a= 3/11 and b=3/2 d. a=3/2 and b=3/11

32. What is the domain of the relation R given by:

a. {1, 2} c. {1, 2, 3}

b. {7, 5} d. {5, 6, 7}

a. {0, 10, 116} c. {2, 12, 24}

b. {0, -10, -116} d. {-2, -12, -24}

35. Which of the following is NOT be a binary operation?

a. addition of integers c. multiplication of integers

b. subtraction of integers d. division of integers

36. A set is _____________under operation if the operation assigns to every ordered pair

of elements from the set an element of the set.

a. associative c. closed

b. commutative d. binary

a. associative c. closed

b. commutative d. binary

38. A binary operation on a finite set can be represented by a table and this table is called:

a. Polya's Table c. Frequency Table

b. Cayley's Table d. Multiplication Table

39. Which of the following is NOT a binary operation?

40. Which of the following is NOT closed in an operation *?

a. 10 c. 12

b. 16 d. -2

a. 28 c. 13

b. 0 d. 54

a. yes c. maybe

b. no d. insufficient information

44. The operation * is defined over the set R (real numbers) by a * b = a + b + 2ab.

What is the identity element under the operation *?

a. 0 c. -1

b. 1 d. 4ab

45 - 49. Refer to a table below:

a. a c. c

b. b d. d

a. a c. c

b. b d. d

a. a c. c

b. b d. d

48. What is its identity?

a. a c. c

b. b d. d

49. What is the inverse of c?

a. a c. c

b. b d. d

IV. Solve the following problems.

50. Tell and explain whether the operation * is a binary operation or not.

51. Show if it is commutative or not.

52. Show if it is associative or not.

53. Find the identity element, if there is.

54. Find the inverse, if there is.

55 - 60. Problem 2. A binary operation * is defined on the set S = {0, 1, 2, 3, 4} by a * b

= a + ab + b. Complete the table below and then answer/solve the following questions/problems.

55. Is it closed under the operation *? Explain.

56. Evaluate (1 * 3) * (2 * 4).

57. Is (2 * 3) = ( 3 * 2)? Explain or write your solution.

58. Is 2 * (3 * 4) equal to (2 * 3) * 4? Explain or write your solution.

59. Find the identity element, if any.

60. Find the inverse, if any.