Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Which of the following are propositions?
", "advice": "For the above we have:
\n1. {all[select[0]][0]}
\n{all[select[0]][1]}
\n2. {all[select[1]][0]}
\n{all[select[1]][1]}
\n3. {all[select[2]][0]}
\n{all[select[2]][1]}
\n4. {all[select[3]][0]}
\n{all[select[3]][1]}
\n5. {all[select[4]][0]}
\n{all[select[4]][1]}
\n6. {all[select[5]][0]}
\n{all[select[5]][1]}
", "rulesets": {}, "extensions": [], "variables": {"marking_matrix": {"name": "marking_matrix", "group": "Ungrouped variables", "definition": "map([all[x][2],all[x][2]*(-1)],x,select)", "description": "", "templateType": "anything"}, "select": {"name": "select", "group": "Ungrouped variables", "definition": "shuffle(list(0..length(all)-1))[0..6]", "description": "", "templateType": "anything"}, "all": {"name": "all", "group": "Ungrouped variables", "definition": "[\n['Every real number is an even integer.','This is a proposition. It is false as there are real numbers which are not even integers, e.g. $1$.',1],\n ['Every even integer is a real number.','A proposition and true.',1],\n ['If $x$ and $y$ are real numbers and $5x=5y$, then $x=y$.','A true proposition as we can cancel off the 5s.',1],\n ['Lions and tigers.','This is not a proposition as there is no truth value we can determine.',-1],\n ['Lions and tigers are animals.','This is a true proposition, at least in the standard interpretation of the words.',1],\n ['Some sets are finite.','A true proposition as, for example, the set $\\\\\\{1 \\\\\\}$ is finite.',1],\n ['The derivative of any polynomial of degree $5$ is a polynomial of degree $6$.','This is a false proposition (as the derivative is of degree $4$).',1],\n ['The smallest positive whole number is 2.','This is a proposition and false, as the smallest positive whole number is $1$.',1],\n ['$\\\\cos(x)=-1$.','This is not a proposition: its truth depends on the value of $x$.',-1],\n ['If $n$ is a real number and $n$ is not zero then $n/n=1$.','This a proposition: it is true.',1],\n ['The integer $x$ is a multiple of $7$.','Not a proposition. Its truth depends on the value of $x$.',-1],\n ['If the integer $x$ is a multiple of $7$, then it is divisible by $7$.','A true proposition.',1],\n ['Either the integer $x$ is a multiple of $7$, or it is not.','A proposition and true.',1],\n ['Call me Ishmael.','Not a proposition as we cannot ascertain a truth value.',-1],\n ['Either $x>3$ or $x<0$.','Not a proposition: its truth depends on the value of $x$.',-1],\n ['They like fishcakes.','Not a proposition. Its truth depends on who \"They\" are.',-1],\n ['In the beginning.','Not a proposition: is neither true nor false.',-1],\n ['This sentence is false. ','Not a proposition. The sentence is self-referential',-1],\n ['To be or not to be.','Not a proposition: is neither true nor false.',-1],\n ['Cork won the Hurling All Ireland in 2005.','A proposition. It is true, according to the records.',1],\n ['Cork and the Rebel county are two different names for the same place.', 'A proposition. It is a true sentence',1],\n ['If $3x^2-2=0$ then $x=\\\\sqrt{2/3}$ or $x=-\\\\sqrt{2/3}$','A proposition. It does not depend what $x$ is. It is true.',1],\n ['Numbers $x$, $y$ and $z$ have the property that $x+y=z$.','Not a proposition, as its truth depends on the values of $x$, $y$ and $z$.',-1],\n ['Numbers $x$, $y$ and $z$ have the property that $x+y>z$ or $x+y \\\\le z$', 'A proposition. One or other of the conditions holds.',1], \n ['Cork is the capital of Ireland','A proposition. Not true but a proposition',1],\n ['It is raining','A proposition. The truth value may change but it is always true or false',1]\n ]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["all", "select", "marking_matrix"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": ["{all[select[0]][0]}", "{all[select[1]][0]}", "{all[select[2]][0]}", "{all[select[3]][0]}", "{all[select[4]][0]}", "{all[select[5]][0]}"], "matrix": "marking_matrix", "layout": {"type": "all", "expression": ""}, "answers": ["Proposition", "Not a proposition"]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}