{"id":12485,"date":"2017-02-11T01:21:15","date_gmt":"2017-02-11T00:21:15","guid":{"rendered":"http:\/\/www.valcon.it\/pp\/?p=12485"},"modified":"2026-07-05T14:38:39","modified_gmt":"2026-07-05T12:38:39","slug":"es2014-5","status":"publish","type":"post","link":"https:\/\/www.valcon.it\/pp\/es2014-5\/","title":{"rendered":"Esame di Stato 2014 &#8211; 5"},"content":{"rendered":"\n<p>Dei numeri 1, 2, 3, \u2026, 6000, quanti non sono divisibili n\u00e9 per 2, n\u00e9 per 3, n\u00e9 per 5?<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Soluzione 1<\/h2>\n\n\n\n<p>Utilizza la <em>forza bruta<\/em><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scrivi i numeri da 1 a 6000<\/li>\n\n\n\n<li>Elimina i multipli di 2<\/li>\n\n\n\n<li>Elimina i multipli di 3<\/li>\n\n\n\n<li>Elimina i multipli di 5<\/li>\n\n\n\n<li>Conta i numeri rimanenti.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">Soluzione 2<\/h2>\n\n\n\n<p>Ricorda che<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Se <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-76cca6cf0833e381e603cdd0450b0d3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#88;&#32;&#92;&#99;&#97;&#112;&#32;&#89;&#32;&#61;&#32;&#92;&#101;&#109;&#112;&#116;&#121;&#115;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: -1px;\"\/> allora <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-a3116cc9811da0ef891276987fff0859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#99;&#117;&#112;&#32;&#89;&#41;&#32;&#61;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#41;&#32;&#43;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#89;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"187\" style=\"vertical-align: -5px;\"\/> altrimenti <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-e06fbb1a98c1c4acee8d795a2d2df6b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#99;&#117;&#112;&#32;&#89;&#41;&#32;&#61;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#41;&#32;&#43;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#89;&#41;&#32;&#45;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#99;&#97;&#112;&#32;&#89;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"279\" style=\"vertical-align: -5px;\"\/><\/li>\n\n\n\n<li>Se <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-0cb0f69e4378bf0beae98770cd0a4812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#89;&#32;&#92;&#115;&#117;&#98;&#115;&#101;&#116;&#101;&#113;&#32;&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: -3px;\"\/> allora <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-3711045ec9ce7b22162b70ea137d72f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#115;&#101;&#116;&#109;&#105;&#110;&#117;&#115;&#32;&#89;&#41;&#32;&#61;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#41;&#32;&#45;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#89;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"184\" style=\"vertical-align: -5px;\"\/> altrimenti <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-3718bd7f1fa63e85b600eb76e5640a1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#115;&#101;&#116;&#109;&#105;&#110;&#117;&#115;&#32;&#89;&#41;&#32;&#61;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#41;&#32;&#45;&#32;&#92;&#115;&#104;&#97;&#114;&#112;&#40;&#88;&#32;&#92;&#99;&#97;&#112;&#32;&#89;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -5px;\"\/><\/li>\n<\/ul>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"264\" height=\"264\" class=\"alignright size-full wp-image-14110\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/uploads\/2014-5-pni.png\" alt=\"\">Osserva l&#8217;immagine a destra<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>#(M2 \u222a M3) = #(M2) + #(M3) &#8211; #(M6)<\/li>\n\n\n\n<li>#(M2 \u222a M5) = #(M2) + #(M5) &#8211; #(M10)<\/li>\n\n\n\n<li>#(M3 \u222a M5) = #(M3) + #(M5) &#8211; #(M15)<\/li>\n\n\n\n<li>#(M6 \u222a M10) = #(M6) + #(M10) &#8211; #(M30)<\/li>\n\n\n\n<li>#(M6 \u222a M15) = #(M6) + #(M15) &#8211; #(M30)<\/li>\n\n\n\n<li>#(M10 \u222a M15) = #(M10) + #(M15) &#8211; #(M30)<\/li>\n\n\n\n<li>#(M6 \u222a M10 \u222a M15) = #(M6) + #(M10) + #(M15) &#8211; 2 * #(M30)<\/li>\n\n\n\n<li>#(M2 \u222a M3 \u222a M5) = #(M2) + #(M3) + #(M5) &#8211; #(M6) &#8211; #(M10) &#8211; #(M15) + #(M30)<\/li>\n<\/ul>\n\n\n\n<p>\u00c8 necessario calcolare la cardinalit\u00e0 di tutti gli insiemi nella tabella<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th>Insieme<\/th><th>Elementi<\/th><th>Cardinalit\u00e0<\/th><th><\/th><\/tr><\/thead><tbody><tr><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-ffcc6ca4cbe68c6f4237bab250a62b47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/><\/td><td>1, 2, 3, 4, &#8230;, 6000<\/td><td>#(<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-ffcc6ca4cbe68c6f4237bab250a62b47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>)<\/td><td>= 6000<\/td><\/tr><tr><td>M2<\/td><td>2, 4, 6, 8, &#8230;, 6000<\/td><td>#(M2)<\/td><td>= 3000<\/td><\/tr><tr><td>M3<\/td><td>3, 6, 9, 12, &#8230;, 6000<\/td><td>#(M3)<\/td><td>= 2000<\/td><\/tr><tr><td>M5<\/td><td>5, 10, 15, 20, &#8230;, 6000<\/td><td>#(M5)<\/td><td>= 1200<\/td><\/tr><tr><td>M6 =&nbsp;M2 \u2229 M3<\/td><td>6, 12, 18, 24, &#8230;, 6000<\/td><td>#(M6)<\/td><td>= 1000<\/td><\/tr><tr><td>M10 = M2 \u2229 M5<\/td><td>10, 20, 30, 40, &#8230;, 6000<\/td><td>#(M10)<\/td><td>= 600<\/td><\/tr><tr><td>M15 = M3 \u2229 M5<\/td><td>15, 30, 45, 60, &#8230;, 6000<\/td><td>#(M15)<\/td><td>= 400<\/td><\/tr><tr><td>M30 = M2 \u2229 M3 \u2229 M5<\/td><td>30, 60, 90, 120, &#8230;, 6000<\/td><td>#(M30)<\/td><td>= 200<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Quindi<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><thead><tr><th>Insieme<\/th><th>Elementi<\/th><th>Cardinalit\u00e0<\/th><th><\/th><\/tr><\/thead><tbody><tr><td>M2&nbsp;\u222a&nbsp;M3&nbsp;\u222a&nbsp;M5<\/td><td>2, 3, 4, 5, &#8230;, 6000<\/td><td>#(M2&nbsp;\u222a&nbsp;M3&nbsp;\u222a&nbsp;M5)<\/td><td>= 3000 + 2000 + 1200 &#8211; 1000 &#8211; 600 &#8211; 400 + 200<br>= <strong>4400<\/strong><\/td><\/tr><tr><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-ffcc6ca4cbe68c6f4237bab250a62b47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> \\ (M2&nbsp;\u222a&nbsp;M3&nbsp;\u222a&nbsp;M5)<\/td><td>1, 7, 11, 13, &#8230;<\/td><td>#(<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-ffcc6ca4cbe68c6f4237bab250a62b47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> \\ (M2&nbsp;\u222a&nbsp;M3&nbsp;\u222a&nbsp;M5))<\/td><td>= 6000 &#8211; 4400<br>= <strong>1600<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Dei numeri 1, 2, 3, \u2026, 6000, quanti non sono divisibili n\u00e9 per 2, n\u00e9 per 3, n\u00e9 per 5? Soluzione 1 Utilizza la forza bruta Soluzione 2 Ricorda che Osserva l&#8217;immagine a destra \u00c8 necessario calcolare la cardinalit\u00e0 di tutti gli insiemi nella tabella Insieme Elementi Cardinalit\u00e0 1, 2, 3, 4, &#8230;, 6000 #() &#8230; <a title=\"Esame di Stato 2014 &#8211; 5\" class=\"read-more\" href=\"https:\/\/www.valcon.it\/pp\/es2014-5\/\" aria-label=\"Per saperne di pi\u00f9 su Esame di Stato 2014 &#8211; 5\">Leggi tutto<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[116],"tags":[],"class_list":["post-12485","post","type-post","status-publish","format-standard","hentry","category-seconda-prova-mat"],"_links":{"self":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/comments?post=12485"}],"version-history":[{"count":26,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12485\/revisions"}],"predecessor-version":[{"id":63936,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12485\/revisions\/63936"}],"wp:attachment":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/media?parent=12485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/categories?post=12485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/tags?post=12485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}