{"id":226925,"date":"2025-06-05T17:06:58","date_gmt":"2025-06-05T17:06:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226925"},"modified":"2025-06-05T17:07:00","modified_gmt":"2025-06-05T17:07:00","slug":"the-second-statement-is-the-of-the-first","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/05\/the-second-statement-is-the-of-the-first\/","title":{"rendered":"The second statement is the of the first"},"content":{"rendered":"\n

The second statement is the of the first. a= b 33 7b contrapositive contradiction inverse converse<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is: C. inverse<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The first statement given is:<\/p>\n\n\n\n

    \n
  • a\u21d2ba \\Rightarrow b<\/li>\n<\/ul>\n\n\n\n

    This is a conditional<\/strong> statement, meaning if a is true, then b is also true<\/em>.<\/p>\n\n\n\n

    The second statement is:<\/p>\n\n\n\n

      \n
    • \u00aca\u21d2\u00acb\\neg a \\Rightarrow \\neg b<\/li>\n<\/ul>\n\n\n\n

      This reads as if not a, then not b<\/em>.<\/p>\n\n\n\n

      This type of transformation is called the inverse<\/strong> of a conditional statement.<\/p>\n\n\n\n

      Let’s break down the four terms to understand why:<\/h4>\n\n\n\n
        \n
      1. Original Statement (Conditional)<\/strong>:
        a\u21d2ba \\Rightarrow b
        “If a, then b.”<\/li>\n\n\n\n
      2. Inverse<\/strong>:
        \u00aca\u21d2\u00acb\\neg a \\Rightarrow \\neg b
        This negates both the hypothesis and the conclusion of the original.
        “If not a, then not b.”
        \u2192 This matches the second statement<\/strong>, so this is the correct answer.<\/li>\n\n\n\n
      3. Converse<\/strong>:
        b\u21d2ab \\Rightarrow a
        This switches the hypothesis and conclusion without negating them.
        “If b, then a.”<\/li>\n\n\n\n
      4. Contrapositive<\/strong>:
        \u00acb\u21d2\u00aca\\neg b \\Rightarrow \\neg a
        This switches and negates both the hypothesis and conclusion.
        “If not b, then not a.”<\/li>\n\n\n\n
      5. Contradiction<\/strong>:
        A contradiction is a logical inconsistency, such as a statement that is always false (e.g., a\u2227\u00acaa \\wedge \\neg a).
        \u2192 This is not what’s happening here.<\/li>\n<\/ol>\n\n\n\n

        Summary:<\/h4>\n\n\n\n
          \n
        • The inverse of a statement a\u21d2ba \\Rightarrow b is \u00aca\u21d2\u00acb\\neg a \\Rightarrow \\neg b.<\/li>\n\n\n\n
        • This does not<\/strong> mean it is logically equivalent to the original statement (only the contrapositive is logically equivalent).<\/li>\n\n\n\n
        • Therefore, the second statement is the inverse<\/strong> of the first.<\/li>\n<\/ul>\n\n\n\n

          \u2705 Correct answer: C. inverse<\/strong><\/p>\n\n\n\n

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

          The second statement is the of the first. a= b 33 7b contrapositive contradiction inverse converse The Correct Answer and Explanation is: The correct answer is: C. inverse Explanation: The first statement given is: This is a conditional statement, meaning if a is true, then b is also true. The second statement is: This reads […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-226925","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226925","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=226925"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226925\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}