{"id":6699,"date":"2011-04-05T22:44:44","date_gmt":"2011-04-05T21:44:44","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6699"},"modified":"2022-01-22T17:27:40","modified_gmt":"2022-01-22T17:27:40","slug":"qual-o-valor-logico-das-proposicoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6699","title":{"rendered":"Qual o valor l\u00f3gico das proposi\u00e7\u00f5es?"},"content":{"rendered":"<p><ul id='GTTabs_ul_6699' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6699' class='GTTabs_curr'><a  id=\"6699_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6699' ><a  id=\"6699_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6699'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Qual o valor l\u00f3gico das proposi\u00e7\u00f5es?<\/p>\n<ol>\n<li>A fun\u00e7\u00e3o $f:x\\to {{x}^{2}}-2$ admite fun\u00e7\u00e3o inversa.<\/li>\n<li>Nenhuma fun\u00e7\u00e3o par admite fun\u00e7\u00e3o inversa.<\/li>\n<li>Algumas fun\u00e7\u00f5es \u00edmpares admitem fun\u00e7\u00e3o inversa.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6699' onClick='GTTabs_show(1,6699)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6699'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>A afirma\u00e7\u00e3o \u00e9 falsa.\n<p>A fun\u00e7\u00e3o $f:x\\to {{x}^{2}}-2$ n\u00e3o admite fun\u00e7\u00e3o inversa, pois n\u00e3o \u00e9 uma fun\u00e7\u00e3o injetiva.<\/p>\n<p>Com efeito, \u00e9 falsa a proposi\u00e7\u00e3o ${{x}_{1}}\\ne {{x}_{2}}\\Rightarrow f({{x}_{1}})\\ne f({{x}_{2}}),\\forall {{x}_{1}},{{x}_{2}}\\in {{D}_{f}}$, j\u00e1 que, por exemplo, $f(-1)=f(1)=-1$.<\/p>\n<\/li>\n<li>A afirma\u00e7\u00e3o \u00e9 verdadeira.\n<p>Se a fun\u00e7\u00e3o \u00e9 par, ent\u00e3o \u00e9 tamb\u00e9m n\u00e3o injetiva. Com efeito, se a fun\u00e7\u00e3o \u00e9 par verifica-se $f(-x)=f(x),\\forall x\\in {{D}_{f}}$, pelo que h\u00e1 objetos diferentes com igual imagem.<\/p>\n<\/li>\n<li>A afirma\u00e7\u00e3o \u00e9 verdadeira.<br \/>\nPor exemplo, a fun\u00e7\u00e3o \u00edmpar de dom\u00ednio $\\mathbb{R}$ definida por $f(x)={{x}^{3}}$ admite inversa, pois \u00e9 injetiva.<\/p>\n<p>Contudo, h\u00e1 fun\u00e7\u00f5es \u00edmpares que n\u00e3o admitem inversa, pois s\u00e3o n\u00e3o injetivas.<br \/>\nPor exemplo:<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6700\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6700\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001.png\" data-orig-size=\"480,360\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001.png\" class=\"aligncenter wp-image-6700 size-full\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001.png\" alt=\"\" width=\"480\" height=\"360\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001.png 480w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001-300x225.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001-150x112.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/05-04-2011-Ecra001-400x300.png 400w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6699' onClick='GTTabs_show(0,6699)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Qual o valor l\u00f3gico das proposi\u00e7\u00f5es? A fun\u00e7\u00e3o $f:x\\to {{x}^{2}}-2$ admite fun\u00e7\u00e3o inversa. Nenhuma fun\u00e7\u00e3o par admite fun\u00e7\u00e3o inversa. Algumas fun\u00e7\u00f5es \u00edmpares admitem fun\u00e7\u00e3o inversa. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20903,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,155],"tags":[156],"series":[],"class_list":["post-6699","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcao-inversa","tag-funcao-inversa-2"],"views":2820,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11V2Pag204-74_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6699","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6699"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6699\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20903"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6699"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}