// Numbas version: finer_feedback_settings
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Remember that $p\\Rightarrow q$ is true whenever $p$ is false or $q$ is true.</p>\n<p></p>", "name": "why parentheses are important for implication", "variable_groups": [], "extensions": [], "ungrouped_variables": [], "functions": {"convch": {"language": "jme", "type": "string", "parameters": [["ch", "string"]], "definition": "switch(ch=\"\\\\neg p\",\"not p[t]\",ch=\"\\\\neg q\",\"not q[t]\",ch=\"p\",\"p[t]\",\"q[t]\")"}, "bool_to_label": {"language": "jme", "type": "number", "parameters": [["l", "list"]], "definition": "map(if(l[x],'T','F'),x,0..length(l)-1)"}, "conv": {"language": "jme", "type": "string", "parameters": [["op", "string"]], "definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")"}, "evaluate": {"language": "javascript", "type": "number", "parameters": [["expr", "string"], ["dependencies", "list"]], "definition": "return scope.evaluate(expr);"}}, "parts": [{"prompt": "<p style=\"text-align: center;\">Complete the following truth table; enter $0$ for false and $1$ for true.<br/><br/></p>\n<table style=\"width: 50px; margin-left: auto; margin-right: auto;\" border=\"1\">\n<tbody>\n<tr><th>$p$</th><th>$q$</th><th>$r$</th><th>$\\quad p\\Rightarrow q\\quad$</th><th style=\"text-align: center;\">$(p\\Rightarrow q)\\Rightarrow r$</th><th>$\\quad q\\Rightarrow r\\quad$</th><th>$p\\Rightarrow (q\\Rightarrow r)$</th><th>$(p\\Rightarrow q)\\wedge (q\\Rightarrow r)$</th></tr>\n<tr>\n<td>0</td>\n<td>0</td>\n<td>0</td>\n<td>[[0]]</td>\n<td>[[8]]</td>\n<td>[[16]]</td>\n<td>[[24]]</td>\n<td>[[32]]</td>\n</tr>\n<tr>\n<td>0</td>\n<td>0</td>\n<td>1</td>\n<td>[[1]]</td>\n<td>[[9]]</td>\n<td>[[17]]</td>\n<td>[[25]]</td>\n<td>[[33]]</td>\n</tr>\n<tr>\n<td>0</td>\n<td>1</td>\n<td>0</td>\n<td>[[2]]</td>\n<td>[[10]]</td>\n<td>[[18]]</td>\n<td>[[26]]</td>\n<td>[[34]]</td>\n</tr>\n<tr>\n<td>0</td>\n<td>1</td>\n<td>1</td>\n<td>[[3]]</td>\n<td>[[11]]</td>\n<td>[[19]]</td>\n<td>[[27]]</td>\n<td>[[35]]</td>\n</tr>\n<tr>\n<td>1</td>\n<td>0</td>\n<td>0</td>\n<td>[[4]]</td>\n<td>[[12]]</td>\n<td>[[20]]</td>\n<td>[[28]]</td>\n<td>[[36]]</td>\n</tr>\n<tr>\n<td>1</td>\n<td>0</td>\n<td>1</td>\n<td>[[5]]</td>\n<td>[[13]]</td>\n<td>[[21]]</td>\n<td>[[29]]</td>\n<td>[[37]]</td>\n</tr>\n<tr>\n<td>1</td>\n<td>1</td>\n<td>0</td>\n<td>[[6]]</td>\n<td>[[14]]</td>\n<td>[[22]]</td>\n<td>[[30]]</td>\n<td>[[38]]</td>\n</tr>\n<tr>\n<td>1</td>\n<td>1</td>\n<td>1</td>\n<td>[[7]]</td>\n<td>[[15]]</td>\n<td>[[23]]</td>\n<td>[[31]]</td>\n<td>[[39]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", 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$p\\Rightarrow q\\Rightarrow r$ without parentheses, and to allow that this is interpreted as `$p\\Rightarrow q$ and $q\\Rightarrow r$ '?</p>", "type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "minMarks": "0", "shuffleChoices": false, "showCorrectAnswer": true, "displayType": "radiogroup", "maxMarks": "5", "matrix": ["0", 0, 0, 0, "5", 0], "variableReplacements": [], "distractors": ["", "", "", "", "", ""], "scripts": {}, "marks": 0, "choices": ["<p>Yes, it is safe and does not matter how this is interpreted because it always means the same.</p>", "<p>Yes, it does not matter how this is interpreted because parentheses usually never matter.</p>", "<p>No, we must not omit the parentheses because every mathematical statement is written including parentheses.</p>", "<p>Yes, it is safe to omit the parentheses because it is clear that this would always mean we first evaluate $p\\Rightarrow q$ and then after that we consider the second implication arrow somehow.</p>\n<p></p>", "<p>No, because no two of the possible interpretations $(p\\Rightarrow q)\\Rightarrow r$ or $p\\Rightarrow (q\\Rightarrow r)$ or $(p\\Rightarrow q)\\wedge (q\\Rightarrow r)$ are equivalent.</p>", "<p>Yes, because two of the interpretations $(p\\Rightarrow q)\\Rightarrow r$ or $p\\Rightarrow (q\\Rightarrow r)$ or $(p\\Rightarrow q)\\wedge (q\\Rightarrow r)$ are equivalent and the third one is usually not considered.</p>"], "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "variables": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>The expression $p\\Rightarrow q\\Rightarrow r$ is ambiguous.</p>"}, "tags": [], "variablesTest": {"maxRuns": "150", "condition": ""}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Bernhard von Stengel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1054/"}]}]}], "contributors": [{"name": "Bernhard von Stengel", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1054/"}]}