In exams: Automatic Generation of Exams in R

# use the same graphics type (pdf, svg, png) as the current xweave() call
typ <- match_exams_device()

# logical operators
ops <- list(
  "or"   = function(a, b) a | b,
  "and"  = function(a, b) a & b,
  "xor"  = function(a, b) !(a & b) & (a | b),
  "nand" = function(a, b) !(a & b),
  "nor"  = function(a, b) !(a | b)
)

# tikz gate
tikz_gate <- function(op) {
  c("\\begin{tikzpicture}[thick]",
    paste0("  \\node[left,draw, logic gate inputs=nn, ", op," gate US,fill=none,,scale=2.5] (G1) at (0,0) {};"),
    "  \\draw (G1.output) --++ (0.5,0) node[right] (y) {$y$};",
    "  \\draw (G1.input 1) --++ (-0.5,0) node[left] {$a$};",
    "  \\draw (G1.input 2) --++ (-0.5,0) node[left] {$b$};",
    "\\end{tikzpicture}")
}

tikz_gate_libraries <- c("arrows", "shapes.gates.logic.US", "calc")

# tikz truth table
tikz_truth_table <- function(op) {
  a <- c(0, 0, 1, 1)
  b <- c(0, 1, 0, 1)
  if(is.character(op)) op <- ops[[op]]

  c("\\node {",
    "  \\begin{tabular}{ccc}\\toprule",
    "    $a$ & $b$ & $y$\\\\",
    "    \\midrule",
    paste("   ", a, "&", b, "&", as.numeric(op(a, b)), "\\\\"),
    "    \\bottomrule",
    "  \\end{tabular}",
    "};")
}

## sample operators
ops4 <- sample(names(ops), 4)
ops3 <- sample(ops4, 3)
ops1 <- sample(ops4, 1)
sol <- ops3 == ops1
sol <- c(sol, !any(sol))
ans <- c("A", "B", "C", "None of these")

## generate all gate images
img <- c(
  include_tikz(tikz_gate(ops3[1]), name = "A", markup = "none", format = typ, library = tikz_gate_libraries),
  include_tikz(tikz_gate(ops3[2]), name = "B", markup = "none", format = typ, library = tikz_gate_libraries),
  include_tikz(tikz_gate(ops3[3]), name = "C", markup = "none", format = typ, library = tikz_gate_libraries)
)

Question

Consider the following gates coding logical operators:

| A | B | C | |:--------------------------:|:--------------------------:|:--------------------------:| | {width=3cm} | {width=3cm} | {width=3cm} |

Which of these gates belongs to the following logical truth table? \

include_tikz(tikz_truth_table(ops1), name = "table", markup = "markdown",
  format = typ, packages = "booktabs", width = "2cm")

answerlist(ans, markup = "markdown")

Solution

The truth table codes the logical r ops1 operator.

The gates displayed code the following logical operators: A = r ops3[1], B = r ops3[2], C = r ops3[3].

Hence, the truth table corresponds to: r ans[sol].

answerlist(ifelse(sol, "True", "False"), markup = "markdown")

Meta-information

exname: Logical operators extype: schoice exsolution: r mchoice2string(sol)

exams documentation built on Oct. 17, 2022, 5:10 p.m.