#import "@local/exam:0.3.0": exam, exercise, exercise-items, horiz-only, mtext

// General configuration
#show: exam.with(
  title: "Exam",

  course-title: [Abstract Binary Computation & Elegant Finite Graphs],

  // Top left header
  institution: [Super University],

  // Top right header
  course-short-title: "ABC & EFG",
  date: "1. January 1970",

  // Exam details, appears below the title
  course-code: "π",
  duration-minutes: "90",

  // Configure personal information fields
  ask-trainer-name: false,
  ask-group: true,
  ask-student-number: false,

  // Configure language, either "de" or "en"
  language: "en",

  // custom instructions
  // instructions: none,

  // change font-size
  // font-size: 12pt,

  // custom paper size
  // paper-size: "a4",

  // custom numbering of exercises
  // exercise-numbering: "1",

  // custom filling lightness for headings
  // fill-luma: 150,
)

// First exercise
#exercise("Relations and their properties", 2)

Consider the relation $R subset NN^2$, defined as follows:

$ (x, y) in R #h(0.5cm) <==> #h(0.5cm) x + y #mtext[is odd]. $

Is $R$ reflexive? transitive? symmetric? antisymmetric?

// Second exercise
#exercise("Properties of functions", 3)

Let $f : (0, +infinity) → (0, +infinity)$ with $f (x) = e^(-x)$.

// Several sub-questions
#exercise-items((
  (1, [Is $f$ injective?]), // The first argument is the number
  // of points the item is worth
  (1, [Is $f$ surjective?]),
  (2, [Is $f$ bijective?]),
))

// Third exercise
#exercise("Logical operators", 3.14)

Consider the following truthtable:

#align(center, table(
  stroke: horiz-only(0.5pt),
  columns: (auto, auto, auto),
  align: center,
  [$A$], [$B$], [$A or B$],
  [1], [1], [1],
  [1], [0], [1],
  [0], [1], [1],
  [0], [0], [1],
))

// More sub-questions
// override-points to false, so that the exercise total points are not recomputed.
#exercise-items(override-points: false, numbering: "i)", (
  (1, [Is the truthtable correct?]),
  (1, [If not, fix it.]),
))