{"id":53006,"date":"2022-04-16T10:29:03","date_gmt":"2022-04-16T10:29:03","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/show-that-the-additive-inverse-or-negative-of-an-even-number-is-an\/"},"modified":"2022-04-16T10:29:03","modified_gmt":"2022-04-16T10:29:03","slug":"show-that-the-additive-inverse-or-negative-of-an-even-number-is-an","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/show-that-the-additive-inverse-or-negative-of-an-even-number-is-an\/","title":{"rendered":"Show that the additive inverse, or negative, of an even number is an"},"content":{"rendered":"<div>\n<p>1. Use a direct proof to show that the sum of two even integers is even.<\/p>\n<p>3. Show that the additive inverse, or negative, of an even number is an even number using a direct proof.<\/p>\n<p>4. Use a direct proof to show that the product of two odd numbers is odd.<\/p>\n<p>5. Prove that if n is a perfect square, then n + 2 is not a perfect square.<\/p>\n<p>6. Use a direct proof to show that the product of two rational numbers is rational.<\/p>\n<p>7. Prove that if m and n are integers and mn is even, then m is even or n is even.<\/p>\n<p>8. Prove that if n is an integer and 3n + 2 is even, then n is even using<\/p>\n<p>a) a proof by contraposition<\/p>\n<p>b) a proof by contradiction<\/p>\n<p>9. Prove the proposition P(1), where P(n) is the proposition \u201cIf n is a positive integer, then n2 \u2265\u00a0n\u201d. What kind of proof did you use?<\/p>\n<p>11. Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.<\/p>\n<p>12. Prove that if n is a positive integer, then n is even if and only if 7n + 4 is even.<\/p>\n<p>13. Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers.<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>1. Use a direct proof to show that the sum of two even integers is even. 3. Show that the additive inverse, or negative, of an even number is an even number using a direct proof. 4. Use a direct proof to show that the product of two odd numbers is odd. 5. Prove that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-53006","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/53006","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=53006"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/53006\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=53006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=53006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=53006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}