{"id":39221,"date":"2025-06-27T04:25:14","date_gmt":"2025-06-27T04:25:14","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39221"},"modified":"2025-06-27T04:25:15","modified_gmt":"2025-06-27T04:25:15","slug":"the-second-statement-is-the-__-of-the-first","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-second-statement-is-the-__-of-the-first\/","title":{"rendered":"The second statement is the __ of the first"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">The second statement is the ____ of the first<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"561\" height=\"301\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-386.png\" alt=\"\" class=\"wp-image-39222\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-386.png 561w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-386-300x161.png 300w\" sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>B. contrapositive<\/strong>.<\/p>\n\n\n\n<p>The original logical statement provided is \u201ca implies b\u201d which is symbolically written as <em>a \u21d2 b<\/em>. The second statement is \u201cnot b implies not a\u201d written as <em>\u00acb \u21d2 \u00aca<\/em>. This second statement is the contrapositive of the first.<\/p>\n\n\n\n<p>To understand this, recall the definitions of related logical forms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>converse<\/strong> of <em>a \u21d2 b<\/em> is <em>b \u21d2 a<\/em>.<\/li>\n\n\n\n<li>The <strong>inverse<\/strong> is <em>\u00aca \u21d2 \u00acb<\/em>.<\/li>\n\n\n\n<li>The <strong>contrapositive<\/strong> is <em>\u00acb \u21d2 \u00aca<\/em>.<\/li>\n<\/ul>\n\n\n\n<p>Contraposition involves two operations: first, negating both the hypothesis and conclusion, and second, switching their order. If you begin with <em>a \u21d2 b<\/em>, its contrapositive becomes <em>\u00acb \u21d2 \u00aca<\/em>. This transformation preserves the logical truth of the original statement. In formal logic, a statement and its contrapositive are always logically equivalent. That means if one is true, so is the other.<\/p>\n\n\n\n<p>To visualize this, suppose <em>a<\/em> stands for \u201cit is raining\u201d and <em>b<\/em> stands for \u201cthe ground is wet.\u201d The statement <em>a \u21d2 b<\/em> reads as \u201cIf it is raining, then the ground is wet.\u201d The contrapositive <em>\u00acb \u21d2 \u00aca<\/em> says, \u201cIf the ground is not wet, then it is not raining.\u201d Both statements convey the same logical relationship.<\/p>\n\n\n\n<p>By contrast, the converse <em>b \u21d2 a<\/em> says \u201cIf the ground is wet, then it is raining.\u201d While that may feel true in some situations, it is not logically equivalent to the original statement. Many other factors could explain the ground being wet.<\/p>\n\n\n\n<p>Thus, the relationship between <em>a \u21d2 b<\/em> and <em>\u00acb \u21d2 \u00aca<\/em> is that of a statement and its contrapositive, which is why the correct answer is B. This distinction is essential in mathematical proofs and logical reasoning.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1140.jpeg\" alt=\"\" class=\"wp-image-39223\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1140.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1140-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1140-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The second statement is the ____ of the first The Correct Answer and Explanation is: The correct answer is B. contrapositive. The original logical statement provided is \u201ca implies b\u201d which is symbolically written as a \u21d2 b. The second statement is \u201cnot b implies not a\u201d written as \u00acb \u21d2 \u00aca. This second statement [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39221","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39221"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39221\/revisions"}],"predecessor-version":[{"id":39224,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39221\/revisions\/39224"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}