{"id":27215,"date":"2025-06-19T21:39:23","date_gmt":"2025-06-19T21:39:23","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27215"},"modified":"2025-06-19T21:39:28","modified_gmt":"2025-06-19T21:39:28","slug":"closure-property-under-subtraction-in-a-set-ensures-that","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/closure-property-under-subtraction-in-a-set-ensures-that\/","title":{"rendered":"Closure property under subtraction in a set ensures that"},"content":{"rendered":"\n<p>Closure property under subtraction in a set ensures that: a) Subtracting any two elements results in a positive number b) Subtracting any two elements results in a number within the set c) Subtracting any two elements results in a negative number d) Subtracting any two elements results in zero<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct answer: b) Subtracting any two elements results in a number within the set<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The closure property refers to whether an operation performed on any two elements of a set always produces a result that also belongs to that set. When discussing the <strong>closure property under subtraction<\/strong>, the focus is on whether <strong>subtracting any two elements<\/strong> from a given set <strong>always<\/strong> results in a number that is <strong>also<\/strong> in that same set.<\/p>\n\n\n\n<p>For a set to be <strong>closed under subtraction<\/strong>, the difference between any two elements taken from the set must still belong to the set. This does <strong>not<\/strong> require the result to be positive, negative, or zero. It only requires the result to <strong>remain inside the set<\/strong>.<\/p>\n\n\n\n<p>Let us consider the following example using the <strong>set of integers<\/strong>, which is closed under subtraction:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 and 3 are both integers.<\/li>\n\n\n\n<li>7 \u2212 3 = 4, which is also an integer.<\/li>\n\n\n\n<li>3 \u2212 7 = \u22124, which is still an integer.<\/li>\n<\/ul>\n\n\n\n<p>No matter which two integers you choose, their difference is always another integer. Hence, integers are closed under subtraction.<\/p>\n\n\n\n<p>Now let us consider the <strong>set of natural numbers<\/strong>, which is <strong>not<\/strong> closed under subtraction:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 and 2 are natural numbers, and 5 \u2212 2 = 3, which is fine.<\/li>\n\n\n\n<li>But 2 \u2212 5 = \u22123, which is <strong>not<\/strong> a natural number, so the closure fails.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the key idea is <strong>not<\/strong> whether the result is positive, negative, or zero, but <strong>whether the result remains in the original set<\/strong>. This is exactly what <strong>option b<\/strong> states.<\/p>\n\n\n\n<p>To summarize, <strong>option b is correct<\/strong> because it directly describes what closure under subtraction means: the result of subtracting any two elements stays within the set.<\/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-banner8-151.jpeg\" alt=\"\" class=\"wp-image-27227\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-151.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-151-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-151-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Closure property under subtraction in a set ensures that: a) Subtracting any two elements results in a positive number b) Subtracting any two elements results in a number within the set c) Subtracting any two elements results in a negative number d) Subtracting any two elements results in zero The Correct Answer and Explanation is: [&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-27215","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27215","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=27215"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27215\/revisions"}],"predecessor-version":[{"id":27228,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27215\/revisions\/27228"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}