Topics: Deductive reasoning (predicate logic)<\/p>\n
Given<\/strong><\/p>\n Every student who studies mathematics has passed calculus. [1] Find<\/strong><\/p>\n Can Alex solve differential equations?<\/p>\n Solution<\/strong><\/p>\n Definition: Representation: Deduction: Answer<\/strong><\/p>\n Yes, Alex can solve differential equations.<\/p>\n","protected":false},"excerpt":{"rendered":" Topics: Deductive reasoning (predicate logic) Given Every student who studies mathematics has passed calculus. [1] Alex is a student. [2]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[47],"tags":[],"_links":{"self":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/19828"}],"collection":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19828"}],"version-history":[{"count":9,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/19828\/revisions"}],"predecessor-version":[{"id":19837,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/19828\/revisions\/19837"}],"wp:attachment":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19828"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19828"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19828"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nAlex is a student. [2]
\nAlex studies mathematics. [3]
\nEveryone who has passed calculus can solve differential equations. [4]<\/p>\n
\n
\n
\nS(x): x is a student.
\nM(x): x studies mathematics.
\nC(x): x has passed calculus.
\nD(x): x can solve differential equations.<\/p>\n
\n[1]: \u2200x(S(x)\u2227M(x)\u2192C(x))
\n[2]: S(Alex)
\n[3]: M(Alex)
\n[4]: \u2200x(C(x)\u2192D(x))<\/p>\n
\nInstantiate x=Alex in [1]: S(Alex)\u2227M(Alex)\u2192C(Alex),
\nwith [2] and [3] we conclude: C(Alex).
\nInstantiate x=Alex in [4]: C(Alex)\u2192D(Alex),
\nwith C(Alex) we conclude: D(Alex).<\/p>\n
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