{"id":90,"date":"2024-03-05T08:47:58","date_gmt":"2024-03-05T16:47:58","guid":{"rendered":"https:\/\/magoosh.com\/lsat\/?p=90"},"modified":"2015-12-11T12:48:25","modified_gmt":"2015-12-11T20:48:25","slug":"ifthen-statements-and-contrapositives-on-the-lsat","status":"publish","type":"post","link":"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/","title":{"rendered":"If\/Then Statements and Contrapositives on the LSAT"},"content":{"rendered":"

Update:<\/b>\u00a0Taking the LSAT in\u00a0August 2024<\/b>\u00a0or later?\u00a0 Be sure you know about\u00a0major upcoming changes to the test and plan accordingly<\/a>.\u00a0 In particular, the Analytical Reasoning section (aka Logic Games) will be removed, and there will be a new argumentative task in the Writing section. Taking the test before August 2024? Read on!<\/p>\n

Formal logic is one of the dreaded monsters of the LSAT, largely because it forces you to pay attention to all those tiny words you usually skim over. If<\/em> is one such word, and it\u2019s definitely one of the most important words to understand on the exam.<\/p>\n

The Standard If\/Then Statement<\/h2>\n

Most people are pretty comfortable with basic if\/then statements. If you\u2019ve ever read a sentence like, \u201cIf today is Valentine\u2019s Day, then it is February,\u201d then you\u2019ve confronted the basic if\/then structure (that was so<\/em> meta). An if\/then statement has two terms. If you know the first term is true, then that is sufficient<\/strong> to know that the second term is true. In other words, if we know today is Valentine\u2019s Day, we don\u2019t need any other information to conclude with certainty that it is currently the month of February.<\/p>\n

On the other hand, knowing that today is February doesn\u2019t necessarily mean it\u2019s Valentine\u2019s Day. It does support the possibility that today is Valentine\u2019s Day, though. In that sense, it\u2019s necessary<\/strong> that today be in the month of February in order for today to be Valentine\u2019s Day.<\/p>\n

So, we can label the first<\/em> term as sufficient<\/strong> to guarantee the truth of the second<\/em> term. We can label the second<\/em> term as necessary<\/strong> to confirm the truth of the first<\/em> term. And that, my friends, is the definition of a necessary vs. sufficient relationship (which, given the order in which they occur in the statement, would be more appropriately called a sufficient vs. necessary relationship, but no one really says it that way).<\/p>\n

Let\u2019s lay it out graphically. The following statements are all logically equivalent.<\/strong><\/p>\n

    \n
  • \n
      If today is Valentine\u2019s Day\u2192 it is currently the month of February<\/ul>\n<\/li>\n<\/ul>\n

       <\/p>\n

        \n
      • \n
          If A\u2192 B<\/ul>\n<\/li>\n<\/ul>\n

           <\/p>\n

            \n
          • \n
              If A is true\u2192 B is definitely true.<\/ul>\n<\/li>\n<\/ul>\n

               <\/p>\n

                \n
              • \n
                  <\/ul>\n<\/li>\n<\/ul>\n

                   <\/p>\n

                    \n
                  • \n
                      If it\u2019s currently February\u2192 it might be Valentine\u2019s Day.<\/ul>\n<\/li>\n<\/ul>\n

                       <\/p>\n

                        \n
                      • \n
                          If B is true\u2192 A might be true.<\/ul>\n<\/li>\n<\/ul>\n

                           <\/p>\n

                            \n
                          • \n
                              <\/ul>\n<\/li>\n<\/ul>\n

                               <\/p>\n

                                \n
                              • \n
                                  If it\u2019s not currently February\u2192 today is definitely not Valentine\u2019s Day.<\/ul>\n<\/li>\n<\/ul>\n

                                   <\/p>\n

                                    If B is not true\u2192 A is definitely not true.<\/ul>\n

                                     <\/p>\n

                                    Contrapositives<\/h2>\n

                                    Those last two sentences are particularly important ones. By taking the two original terms, swapping their order, and negating both of them, we have formed the contrapositive<\/strong> of the original if\/then statement. The contrapositive is always logically equivalent to the original statemen<\/strong>t (in other words, it must be true). In fact, the contrapositive is the only other absolute certainty we can draw from an if\/then statement:<\/p>\n

                                    If we know that today is Valentine\u2019s Day, that is sufficient to know for sure that it\u2019s also February.
                                    \nIn order for today to be Valentine\u2019s Day, it\u2019s necessary that today is in the month of February.
                                    \nThus, if today is not in the month of February, there\u2019s no way that today could be Valentine\u2019s Day, and that\u2019s our contrapostive!<\/p>\n

                                    Contrapositives are valuable on the LSAT because they provide us with a piece of information that is not explicitly stated but is definitely true. Thus, they allow you to reach conclusions that you couldn\u2019t reach if you used only what is written on the page.<\/p>\n

                                    However, contrapositives can be dangerous if you\u2019re not careful. It\u2019s very easy to draw a false conclusion from an if\/then statement by forming your contrapositive incorrectly. Here are the most common mistakes people make when forming a contrapositive:<\/p>\n

                                      \n
                                    1. \n
                                        \n
                                      1. Swapping the terms but not negating them.<\/strong>
                                        \nThis is like saying, \u201cIf it\u2019s currently February, then it\u2019s Valentine\u2019s Day.\u201d Sure, it could be Valentine\u2019s Day, but it could also be any other day in February.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                         <\/p>\n

                                          \n
                                        1. \n
                                            \n
                                          1. Negating the terms but not swapping them.<\/strong>
                                            \nThis is like saying, \u201cIf it\u2019s not Valentine\u2019s Day, then it\u2019s not February.\u201d Again, this could be
                                            \ntrue because it could be June or September or December, but it also might be any day in
                                            \nFebruary other than Valentine\u2019s Day.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                             <\/p>\n

                                              \n
                                            1. \n
                                                \n
                                              1. Applying a false \u201ctrigger\u201d.<\/strong>
                                                \nLogically, doing this means you\u2019re making one of the two previous mistakes, but it\u2019s a bit
                                                \nmore subtle. Read on for an explanation.<\/p>\n

                                                Triggers<\/h2>\n

                                                A \u201ctrigger\u201d is a term in an if\/then statement that guarantees a certain result. It\u2019s the first term in a standard if\/then statement. However, there are other forms of if\/thens in which the trigger could appear as the second term. I talk about those in this blog post, so check it out if you\u2019re interested.
                                                \nApplying a false trigger means you\u2019re using the second term as a trigger or you\u2019re
                                                \nsomehow changing the first term. For example, the trigger in \u201cIf it\u2019s Valentine\u2019s Day, then it\u2019s February\u201d is knowing that today is Valentine\u2019s Day. If today is not Valentine\u2019s Day, we don\u2019t know anything else for certain. Likewise, if today is February, we don\u2019t know really know anything else about the day. But, if today is not February, we do know that it\u2019s also not Valentine\u2019s Day. This is because \u201cnot February\u201d is the trigger in our contrapositive.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                 <\/p>\n

                                                So remember these two things about if\/then statements<\/strong>:<\/p>\n

                                                  \n
                                                1. \n
                                                    \n
                                                  1. \n
                                                      Contrapositives need to be crafted carefully by swapping and negating both terms in your if\/then statement.<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                       <\/p>\n

                                                        \n
                                                      1. \n
                                                          \n
                                                        1. \n
                                                            <\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                             <\/p>\n

                                                              \n
                                                            1. \n
                                                                \n
                                                              1. \n
                                                                  Only the first term in a standard if\/then statement is a trigger, and it needs to be interpreted narrowly. Negating the trigger, or using the result as a trigger, will bring you to a possible, but not necessary, conclusion.<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                   <\/p>\n","protected":false},"excerpt":{"rendered":"

                                                                  Update:\u00a0Taking the LSAT in\u00a0August 2024\u00a0or later?\u00a0 Be sure you know about\u00a0major upcoming changes to the test and plan accordingly.\u00a0 In particular, the Analytical Reasoning section (aka Logic Games) will be removed, and there will be a new argumentative task in the Writing section. Taking the test before August 2024? Read on! Formal logic is one […]<\/p>\n","protected":false},"author":123,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"ppma_author":[3856],"class_list":["post-90","post","type-post","status-publish","format-standard","hentry","category-logic-games"],"acf":[],"yoast_head":"\nIf\/Then Statements and Contrapositives on the LSAT - Magoosh LSAT Blog<\/title>\n<meta name=\"description\" content=\"Post covering the basics of how to interpret if\/then statements, including constructing contrapositives and determining necessary vs. sufficient terms.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If\/Then Statements and Contrapositives on the LSAT\" \/>\n<meta property=\"og:description\" content=\"Update:\u00a0Taking the LSAT in\u00a0August 2024\u00a0or later?\u00a0 Be sure you know about\u00a0major upcoming changes to the test and plan accordingly.\u00a0 In particular, the\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh LSAT Blog\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-05T16:47:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2015-12-11T20:48:25+00:00\" \/>\n<meta name=\"author\" content=\"Travis Coleman\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Travis Coleman\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\"},\"author\":{\"name\":\"Travis Coleman\",\"@id\":\"https:\/\/magoosh.com\/lsat\/#\/schema\/person\/2b0d4d89a6af649558a6201c09bd4254\"},\"headline\":\"If\/Then Statements and Contrapositives on the LSAT\",\"datePublished\":\"2024-03-05T16:47:58+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\"},\"wordCount\":1007,\"commentCount\":2,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/lsat\/#organization\"},\"articleSection\":[\"Logic Games (Analytical Reasoning)\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\",\"url\":\"https:\/\/magoosh.com\/lsat\/ifthen-statements-and-contrapositives-on-the-lsat\/\",\"name\":\"If\/Then Statements and Contrapositives on the LSAT - 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With a JD from NYU and an English degree from Boston College, he's dedicated his career to fighting the forces of unnecessary legal jargon and faulty logic. When not geeking out on the LSAT, he can probably be found on skis, in water, or in the vicinity of a roller coaster.","url":"https:\/\/magoosh.com\/lsat\/author\/travis\/"}]}},"authors":[{"term_id":3856,"user_id":123,"is_guest":0,"slug":"travis","display_name":"Travis Coleman","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/bb41577b3ff13e68b090cc8fc881c3595171b630d81eb41d5e2911416566e0d2?s=96&d=mm&r=g","user_url":"","last_name":"Coleman","first_name":"Travis","description":"Travis is in charge of helping students turn <a href=\"http:\/\/i.imgur.com\/5wS378R.jpg\">LSAT prep<\/a> into an afternoon with <a href=\"http:\/\/media.tumblr.com\/e1d7ee244427c371aab703630cd9f6a4\/tumblr_inline_ncf9xfqVJx1riqfqx.jpg\">this guy<\/a>. With a JD from NYU and an English degree from Boston College, he's dedicated his career to fighting the forces of unnecessary legal jargon and faulty logic. When not geeking out on the LSAT, he can probably be found on skis, in water, or in the vicinity of a roller coaster."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/posts\/90","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/users\/123"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/comments?post=90"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/posts\/90\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/media?parent=90"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/categories?post=90"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/tags?post=90"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/lsat\/wp-json\/wp\/v2\/ppma_author?post=90"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}