[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-178927-105":59,"doc-detail-178927-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","conditional-statements-translating-conditional-statements","Conditional Statements - Translating Conditional Statements","","Conditional logic practice focuses on understanding statements like “All A are B,” “If A then B,” and “Unless A, not B,” then identifying their correct interpretations. The material uses short everyday scenarios (ducks and water, Tuesday and going to work, Americans and loving cheese, dates and funny guys, whales and loving music) to illustrate how to translate between original statements and logical forms. Exercises include matching forms, using contrapositive reasoning, and selecting gap fillers that eliminate support-point gaps.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/conditional-statements-translating-conditional-statements/178927/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/conditional-statements-translating-conditional-statements/178927.png","ImageObject",300,407,{"name":92,"@type":93},"Rhys","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-07","2026-09-02",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the exercise “Translating Conditional Statements” require you to do?","Question",{"text":112,"@type":113},"Match each conditional or quantified statement with its correct logical interpretation, choosing the option that accurately represents the “if/only if/unless” structure.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do contrapositive rules help in the drills?",{"text":117,"@type":113},"Contrapositives let you rewrite statements into an equivalent form, such as turning “If P then Q” into “If not Q then not P,” making the correct relationship easier to verify.",{"name":119,"@type":110,"acceptedAnswer":120},"Why do some potential gap fillers fail in the “fill the hole” examples?",{"text":121,"@type":113},"Incorrect fillers leave mismatches between the support and the point—meaning they do not fully connect the required conditions and conclusions without leaving a gap.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},178927,1789978467,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","| Sharon must be great at figuring out mysteries. After all, she is the police chief. | All carnivores eat meat. Therefore, all carnivores eat beef. | fill the hole |\n| --- | --- | --- |\n| Bill is a vegetarian. For that reason, he must hate the taste of meat. | Most Texans own hats. Therefore, some Texans own hat racks. | Think about the point, the support, and the hole between the two. Try to come up with answers that will completely fill the hole—answers that leave no gap between the support and the point. |\n\n\n| Here are a few of the many ways we could represent the gap fillers:\u003Cbr>The police chief is required to be good at figuring out mysteries.(+A bit more) All police chiefs are great at solving mysteries.\u003Cbr>Bill is a vegetarian only if he hates the taste of meat.•(+ A bit more) Every vegetarian hates the taste of meat.\u003Cbr>All people who eat meat eat beef\u003Cbr>Every persona who owns hats owns a hat rack.\u003Cbr>a Can you see why “some people” or“most people” wouldn’t fill the gap? Neither would ensure that Texans own hat racks. |\n| --- |\n| 1. contrapositives |\n| Those who are not good at figuring out mysteries cannot be police officers.\u003Cbr>Those who do not hate the taste of meat are never vegetarians.\u003Cbr>If you don’t eat beef, you don’t eat any meat at all.\u003Cbr>No one without a hat rack owns a hat. |\n\n| EXAMPLES\u003Cbr>“Every American likes television.”\u003Cbr>Does this guarantee that if you like television, you are American? No. Does it guarantee that if you are American, you like television? Yes.\u003Cbr>American → like television\u003Cbr>“Getting into the house requires a key.”\u003Cbr>Does this mean that if you have a key you are guaranteed to get into the house? No. (Maybe you had the wrong key.) Does this mean that if you get into the house you are guaranteed to have had a key? Yes.\u003Cbr>Get in → have key\u003Cbr>“No act can be seen as altruism unless the person seeing it is himself selfless.”\u003Cbr>Does this mean that if you see an act as altruistic, you are selfless? Hmmm. Does this mean that if you are selfless, you will see an act as altruistic? Hmmm. Does this mean if you are not selfless, you will not see an act as altruistic? Hmmm. Let’s stop there. If you feel like you are turned around enough to possibly make a mistake, consider quickly how the statement relates to your conditional mantra. |  |\n| --- | --- |\n| We know...\u003Cbr>“You can’t drive unless you are at least sixteen.” | So...\u003Cbr>“No act can be seen as altruism unless the person seeing it is himself selfless.” |\n| is\u003Cbr>Drive → at least 16 | must be altruism → selfless |\n| Yes! We nailed it! Having a mantra to structure your thinking can help you when the abstract situation makes jelly out of your internal conditional sense. |  |\n\n\n| Drill: Translating Conditional Statements |  |  |\n| --- | --- | --- |\n| Directions: Match the statement to the correct interpretation. |  |  |\n| D →W, ~~W~~ → ~~ D~~  | D = DUCK W = LIKE WATER\u003Cbr>1. All ducks like water.\u003Cbr>2. If you like water, you are a duck.\u003Cbr>3. No duck doesn’t like water.\u003Cbr>4. Every animal that likes water is a duck.\u003Cbr>5. No duck likes water.\u003Cbr>6. Any animal that likes water is not a duck.\u003Cbr>7. Unless an animal is a duck, it will not like water.\u003Cbr>8. Ducks need to like water. | W → D, ~~ D~~ →~~W~~ |\n| D →~~W~~, W → ~~ D~~ | 9. One does not like water only if one is a duck.\u003Cbr>10. In order to like water, you must be a duck. | ~~D~~ →W, ~~W~~ → D |\n| T →W, ~~W~~ → ~~T~~ | T = TUESDAY W = GO TO WORK\u003Cbr>1. If it’s Tuesday, I’ll go to work.\u003Cbr>2. I never go to work on Tuesday.\u003Cbr>3. I’ll go to work only if it’s Tuesday.\u003Cbr>4. Unless it is Tuesday, I will go to work.\u003Cbr>5. I go to work every Tuesday.\u003Cbr>6. I only work on Tuesdays.\u003Cbr>7. Any day that I am not working is not a Tuesday.\u003Cbr>8. If it’s not Tuesday, I don’t work. | W →T, ~~T~~ → ~~W~~ |\n| T →~~W~~, W → ~~T~~ | 9. All Tuesdays are days I go to work.\u003Cbr>10. Any day I go to work is a Tuesday. | ~~T~~ →W, ~~W~~ → T |\n| A →C, ~~C~~ → ~~A~~ | A = AMERICAN C = LOVES CHEESE\u003Cbr>1. Every","cbCaiqQzC7KqW4Ue","https://ap.wps.com/l/cbCaiqQzC7KqW4Ue","pdf",365029,18,"English","# Translating Conditional Statements\n## Matching statements to interpretations\n## Contrapositives and gap-fill reasoning\n## Practice drills with examples","[{\"question\":\"What does the exercise “Translating Conditional Statements” require you to do?\",\"answer\":\"Match each conditional or quantified statement with its correct logical interpretation, choosing the option that accurately represents the “if/only if/unless” structure.\"},{\"question\":\"How do contrapositive rules help in the drills?\",\"answer\":\"Contrapositives let you rewrite statements into an equivalent form, such as turning “If P then Q” into “If not Q then not P,” making the correct relationship easier to verify.\"},{\"question\":\"Why do some potential gap fillers fail in the “fill the hole” examples?\",\"answer\":\"Incorrect fillers leave mismatches between the support and the point—meaning they do not fully connect the required conditions and conclusions without leaving a gap.\"}]","Conditional Statements - Translating Conditional Statements | PDF",1788334528,45]