a) The line
\nz = x & !y\n
tells us that $z$ is true if $x$ is true and $y$ is false.
\nb) It follows from part (a) that $a$ is true if $z$ is false and $a$ is false if $z$ is true.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": ["1", "1"], "shuffleChoices": false, "variableReplacements": [], "choices": ["TRUE
FALSE
What is the value of $a$?
", "matrix": [0, "1"], "shuffleChoices": false, "variableReplacements": [], "choices": ["TRUE
FALSE
> x = TRUE", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 13 TRUE/FALSE", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": ["a"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> y = FALSE
> z = x & !y
> a = !z
We are given that x = TRUE, y = FALSE.
The line
x = (y|!y) & x
\nsays, x is true if both of the following are true: y is either true or false, and x is true.
\nThen,
\nz = x
sets $z$ to be equal to $x$, hence its earlier value is irrelevant.
What is the value of $z$?
", "matrix": [0, 0, "1"], "shuffleChoices": false, "variableReplacements": [], "choices": ["{a}
", "FALSE
TRUE
> x = TRUE", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-20..20#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 14 Sequences selecting greater than etc", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> y = FALSE
> z = {a}
> x = (y|!y) & x
> z = x
$x$ is a sequence between -2 and 10.
\n$z$ selects the values from $x$ that are greater than or equal to 7.
\n$y$ selects the values from $x$ that are greater than or equal to 7 OR less than 0.
\n$a$ selects the elements of $y$ that are equal to -2. So if $y$ = -2 -1 7 8 9 10 it is the first element that is equal to -2.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": [0, "1", 0, 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["TRUE
7 8 9 10
", "0 1 2 3 4 5 6
", "FALSE TRUE TRUE
What is the value of $y$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["-2 -1 7 8 9 10
", "TRUE
7 8 9 10
", "-2 -1
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $a$?
", "matrix": [0, 0, "1", 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["-2
", "4
", "1
", "TRUE
> x = seq(-2, 10)", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 14 Sequences selecting greater than etc", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> z = x[(x >= 7) ]
> y = x[(x >= 7) | x < 0]
> a = which(y==-2)
$x$ is a sequence between -5 and 5.
\n$z$ selects the values from $x$ that are less than -2.
\n$y$ selects the values from $x$ that are greater than or equal to 3 OR less than -2.
\n$a$ selects the indices of the value in $z$ that is equal to -3. So if $z$ = -5 -4 -3 it is the third indices that is equal to -3.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": [0, "1", 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["TRUE
-5 -4 -3
", "-5 -4 -3 -2
", "FALSE TRUE TRUE
What is the value of $y$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["-5 -4 -3 3 4 5
", "TRUE
3 4 5
", "-5 -4 -3
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $a$?
", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["3
", "-5 -4 -3
", "-3
", "TRUE
> x = seq(-5, 5)", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 15 what type of variable", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> z = x[(x < -2) ]
> y = x[(x >= 3) | x < -2]
> a = which(z==-3)
a) To check this use the command 'is.data.frame(m1)'
\nb) To check this use the commands 'is.vector(m2)' to show m2 is a vector and then 'is.logical(m2)' to show it is logical.
", "rulesets": {}, "parts": [{"distractors": ["", "", "", ""], "prompt": "What type of variable is m1?
", "matrix": [0, 0, 0, "1"], "shuffleChoices": false, "scripts": {}, "choices": ["A vector of doubles
", "A vector of Logical
", "A vector of string
", "A dataframe
"], "displayType": "radiogroup", "maxMarks": "1", "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"distractors": ["", "", "", ""], "prompt": "What type of variable is m2?
", "matrix": [0, "1", 0, 0], "shuffleChoices": false, "scripts": {}, "choices": ["A vector of doubles
", "A vector of Logicals
", "A vector of string
", "A data frame
"], "displayType": "radiogroup", "maxMarks": "1", "marks": 0, "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "> m1 = movies[movies$Budget > 10000,]", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Question 16 vector mean and range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> m2 = movies$Budget > 10000
The function c combines the numbers in its argument into a vector, which in this case is assigned to $x$
\na)
\nThe function mean returns, as expected, the mean of the values in its argument.
\nb)
\nThe function range returns a vector containing the minimum and maximum of its argument, in this case the minimum and maximum of $x$, so $1$ and $6$. In fact we could have answered this without any further information; this was the only possible answer, as we expected a vector with 2 elements.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $y$?
", "matrix": [0, "1", 0, 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["$\\frac{7}{4}$
", "$\\frac{7}{2}$
", "$\\frac{6}{4}$
", "$\\frac{5}{3}$
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": [0, 0, "1", 0], "shuffleChoices": false, "variableReplacements": [], "choices": ["1 2 3 4 5 6
", "5
", "1 6
", "6
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "> x = c(1,2,3,4,5,6)", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Amy's copy of Question 16 vector mean and range", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "
> y = mean(x)
> z = range(x)
x=1:10 creates a vector $x$ with 10 elements from 1 to 10.
\na)
\nThe function mean returns, as expected, the mean of the values in its argument, in this case the mean of the elements in the vector $x$.
\nb)
\nThe length function returns the length of its argument, in this case the number of elements in $x$.
", "rulesets": {}, "parts": [{"displayColumns": 0, "prompt": "What is the value of $y$?
", "matrix": ["1", "0", 0, 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["$\\frac{11}{2}$
", "$\\frac{11}{4}$
", "$\\frac{1}{2}$
", "$\\frac{10}{2}$
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"displayColumns": 0, "prompt": "What is the value of $z$?
", "matrix": [0, "1", "0", 0], "shuffleChoices": true, "variableReplacements": [], "choices": ["1 2 3 4 5 6 7 8 9 10
", "10
", "1 10
", "2
"], "variableReplacementStrategy": "originalfirst", "maxMarks": "1", "distractors": ["", "", "", ""], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}], "statement": "> x = 1:10", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}], "extensions": [], "custom_part_types": [], "resources": []}
> y = mean(x)
> z = length(x)