{"id":1264,"date":"2015-10-15T08:07:30","date_gmt":"2015-10-15T07:07:30","guid":{"rendered":"http:\/\/www.venco.com.pl\/~cozy\/blog\/?p=1264"},"modified":"2015-10-15T08:07:30","modified_gmt":"2015-10-15T07:07:30","slug":"symbole-logiczne","status":"publish","type":"post","link":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/2015\/10\/15\/symbole-logiczne\/","title":{"rendered":"Symbole logiczne"},"content":{"rendered":"

Basic logic symbols<\/span><\/h2>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n
Symbol<\/div>\n<\/th>\n
Name<\/th>\nExplanation<\/th>\nExamples<\/th>\nUnicode
\nValue<\/th>\n		HTML
\nName<\/th>\n		LaTeX<\/a>
\nsymbol<\/th>\n<\/tr>\n
Read as<\/th>\n<\/tr>\n
Category<\/th>\n<\/tr>\n
\n
\u21d2<\/p>\n

\u2192<\/p>\n

\u2283<\/p><\/div>\n<\/td>\n

material implication<\/a><\/td>\nA<\/i> \u21d2 B<\/i> is true only in the case that either A<\/i> is false or B<\/i> is true.<\/p>\n

\u2192 may mean the same as \u21d2 (the symbol may also indicate the domain and codomain of a function<\/a>; see table of mathematical symbols<\/a>).<\/p>\n

\u2283 may mean the same as \u21d2 (the symbol may also mean superset<\/a>).<\/td>\n

x<\/i> = 2\u00a0\u00a0\u21d2\u00a0 x<\/i>2<\/sup> = 4 is true, but x<\/i>2<\/sup> = 4 \u00a0\u00a0\u21d2\u00a0 x<\/i> = 2 is in general false (since x<\/i> could be \u22122).<\/td>\nU+21D2<\/p>\n

U+2192<\/p>\n

U+2283<\/th>\n

&rArr;<\/p>\n

&rarr;<\/p>\n

&sup;<\/th>\n

\n
\"\\Rightarrow\"\\Rightarrow
\n\"\\to\"\\to
\n\"\\supset\"\\supset
\n\"\\implies\"\\implies<\/div>\n<\/th>\n<\/tr>\n
implies; if .. then<\/td>\n<\/tr>\n
propositional logic<\/a>, Heyting algebra<\/a><\/td>\n<\/tr>\n
\n
\u21d4<\/p>\n

\u2261<\/p>\n

↔<\/p><\/div>\n<\/td>\n

material equivalence<\/a><\/td>\nA<\/i>\u00a0\u21d4 B<\/i> is true only if both A<\/i> and B<\/i> are false, or both A<\/i> and B<\/i> are true.<\/td>\nx<\/i>\u00a0+\u00a05\u00a0=\u00a0y<\/i>\u00a0+\u00a02\u00a0\u00a0\u21d4\u00a0\u00a0x<\/i>\u00a0+\u00a03\u00a0= y<\/i><\/td>\nU+21D4<\/p>\n

U+2261<\/p>\n

U+2194<\/th>\n

&hArr;<\/p>\n

&equiv;<\/p>\n

&harr;<\/th>\n

\n
\"\\Leftrightarrow\"\\Leftrightarrow
\n\"\\equiv\"\\equiv
\n\"\\leftrightarrow\"\\leftrightarrow
\n\"\\iff\"\\iff<\/div>\n<\/th>\n<\/tr>\n
if and only if; iff; means the same as<\/td>\n<\/tr>\n
propositional logic<\/a><\/td>\n<\/tr>\n
\n
\u00ac<\/p>\n

\u02dc<\/p>\n

!<\/p><\/div>\n<\/td>\n

negation<\/a><\/td>\nThe statement \u00acA<\/i> is true if and only if A<\/i> is false.<\/p>\n

A slash placed through another operator is the same as „\u00ac” placed in front.<\/td>\n

\u00ac(\u00acA<\/i>)\u00a0\u21d4 A<\/i>
\nx<\/i>\u00a0\u2260\u00a0y<\/i>\u00a0\u00a0\u21d4\u00a0 \u00ac(x<\/i>\u00a0=\u00a0y<\/i>)<\/td>\n		U+00AC<\/p>\n

U+02DC<\/th>\n

&not;<\/p>\n

&tilde; ~<\/th>\n

\n
\"\\neg\"\\lnot or \\neg
\n\"\\sim\"\\sim<\/div>\n<\/th>\n<\/tr>\n
not<\/td>\n<\/tr>\n
propositional logic<\/a><\/td>\n<\/tr>\n
\n
\u2227<\/p>\n

\u2022<\/p>\n

&<\/p><\/div>\n<\/td>\n

logical conjunction<\/a><\/td>\nThe statement A<\/i> \u2227 B<\/i> is true if A<\/i> and B<\/i> are both true; else it is false.<\/td>\nn<\/i>\u00a0< 4\u00a0\u00a0\u2227\u00a0 n<\/i>\u00a0>2\u00a0\u00a0\u21d4\u00a0 n<\/i>\u00a0= 3 when n<\/i> is a natural number<\/a>.<\/td>\nU+2227<\/p>\n

U+0026<\/th>\n

&and;<\/p>\n

&amp;<\/th>\n

\"\\wedge\"\\wedge or \\land
\n\\&[2]<\/a><\/sup><\/th>\n<\/tr>\n
and<\/td>\n<\/tr>\n
propositional logic<\/a>, Boolean algebra<\/a><\/td>\n<\/tr>\n
\n
\u2228<\/p>\n

+<\/p>\n

\u01c0\u01c0<\/p><\/div>\n<\/td>\n

logical (inclusive) disjunction<\/a><\/td>\nThe statement A<\/i> \u2228 B<\/i> is true if A<\/i> or B<\/i> (or both) are true; if both are false, the statement is false.<\/td>\nn<\/i>\u00a0\u2265 4\u00a0\u00a0\u2228\u00a0 n<\/i>\u00a0\u2264 2\u00a0\u00a0\u21d4 n<\/i>\u00a0\u2260 3 when n<\/i> is a natural number<\/a>.<\/td>\nU+2228<\/th>\n&or;<\/th>\n\"\\lor\"\\lor or \\vee<\/th>\n<\/tr>\n
or<\/td>\n<\/tr>\n
propositional logic<\/a>, Boolean algebra<\/a><\/td>\n<\/tr>\n
\n
\u2295<\/p>\n

\u22bb<\/span><\/div>\n<\/td>\n

exclusive disjunction<\/a><\/td>\nThe statement A<\/i> \u2295 B<\/i> is true when either A or B, but not both, are true. A<\/i> \u22bb<\/span> B<\/i> means the same.<\/td>\n(\u00acA<\/i>) \u2295 A<\/i> is always true, A<\/i> \u2295 A<\/i> is always false.<\/td>\nU+2295<\/p>\n

U+22BB<\/th>\n

&oplus;<\/th>\n\"\\oplus\"\\oplus
\n\"\\veebar\"\\veebar<\/th>\n<\/tr>\n
xor<\/td>\n<\/tr>\n
propositional logic<\/a>, Boolean algebra<\/a><\/td>\n<\/tr>\n
\n
\u22a4<\/p>\n

T<\/p>\n

1<\/p><\/div>\n<\/td>\n

Tautology<\/a><\/td>\nThe statement \u22a4 is unconditionally true.<\/td>\nA<\/i> \u21d2 \u22a4 is always true.<\/td>\nU+22A4<\/th>\nT<\/th>\n\"\\top\"\\top<\/th>\n<\/tr>\n
top, verum<\/td>\n<\/tr>\n
propositional logic<\/a>, Boolean algebra<\/a><\/td>\n<\/tr>\n
\n
\u22a5<\/p>\n

F<\/p>\n

0<\/p><\/div>\n<\/td>\n

Contradiction<\/a><\/td>\nThe statement \u22a5 is unconditionally false.<\/td>\n\u22a5 \u21d2 A<\/i> is always true.<\/td>\nU+22A5<\/th>\n&perp; F<\/th>\n\"\\bot\"\\bot<\/th>\n<\/tr>\n
bottom, falsum, falsity<\/td>\n<\/tr>\n
propositional logic<\/a>, Boolean algebra<\/a><\/td>\n<\/tr>\n
\n
\u2200<\/p>\n

()<\/p><\/div>\n<\/td>\n

universal quantification<\/a><\/td>\n\u2200\u00a0x<\/i>:\u00a0P<\/i>(x<\/i>) or (x<\/i>)\u00a0P<\/i>(x<\/i>) means P<\/i>(x<\/i>) is true for all x<\/i>.<\/td>\n\u2200\u00a0n<\/i>\u00a0\u2208 \u2115<\/span>: n<\/i>2<\/sup>\u00a0\u2265 n<\/i>.<\/td>\nU+2200<\/th>\n&forall;<\/th>\n\"\\forall\"\\forall<\/th>\n<\/tr>\n
for all; for any; for each<\/td>\n<\/tr>\n
first-order logic<\/a><\/td>\n<\/tr>\n
\n
\u2203<\/div>\n<\/td>\n
existential quantification<\/a><\/td>\n\u2203\u00a0x<\/i>: P<\/i>(x<\/i>) means there is at least one x<\/i> such that P<\/i>(x<\/i>) is true.<\/td>\n\u2203\u00a0n<\/i>\u00a0\u2208 \u2115<\/span>: n<\/i> is even.<\/td>\nU+2203<\/a><\/th>\n&exist;<\/th>\n\"\\exists\"\\exists<\/th>\n<\/tr>\n
there exists<\/td>\n<\/tr>\n
first-order logic<\/a><\/td>\n<\/tr>\n
\n
\u2203!<\/div>\n<\/td>\n
uniqueness quantification<\/a><\/td>\n\u2203!\u00a0x<\/i>: P<\/i>(x<\/i>) means there is exactly one x<\/i> such that P<\/i>(x<\/i>) is true.<\/td>\n\u2203!\u00a0n<\/i>\u00a0\u2208 \u2115<\/span>: n<\/i>\u00a0+ 5\u00a0= 2n<\/i>.<\/td>\nU+2203\u00a0U+0021<\/th>\n&exist;\u00a0!<\/th>\n\"\\exists\\exists\u00a0!<\/th>\n<\/tr>\n
there exists exactly one<\/td>\n<\/tr>\n
first-order logic<\/a><\/td>\n<\/tr>\n
\n
:=<\/p>\n

\u2261<\/p>\n

:\u21d4<\/p><\/div>\n<\/td>\n

definition<\/a><\/td>\nx<\/i>\u00a0:= y<\/i> or x<\/i>\u00a0\u2261 y<\/i> means x<\/i> is defined to be another name for y<\/i> (but note that \u2261 can also mean other things, such as congruence<\/a>).<\/p>\n

P<\/i>\u00a0:\u21d4 Q<\/i> means P<\/i> is defined to be logically equivalent<\/a> to Q<\/i>.<\/td>\n

cosh\u00a0x<\/i>\u00a0:= (1\/2)(exp\u00a0x<\/i>\u00a0+ exp\u00a0(\u2212x<\/i>))<\/p>\n

A<\/i>\u00a0XOR\u00a0B<\/i>\u00a0:\u21d4 (A<\/i>\u00a0\u2228\u00a0B<\/i>)\u00a0\u2227\u00a0\u00ac(A<\/i>\u00a0\u2227\u00a0B<\/i>)<\/td>\n

U+2254 (U+003A\u00a0U+003D)<\/p>\n

U+2261<\/p>\n

U+003A\u00a0U+229C<\/th>\n

:=
\n:<\/p>\n

&equiv;<\/p>\n

&hArr;<\/th>\n

\n
\":=\":=
\n\"\\equiv\"\\equiv
\n\"\\Leftrightarrow\"\\Leftrightarrow<\/div>\n<\/th>\n<\/tr>\n
is defined as<\/td>\n<\/tr>\n
everywhere<\/td>\n<\/tr>\n
\n
( )<\/div>\n<\/td>\n
precedence grouping<\/td>\nPerform the operations inside the parentheses first.<\/td>\n(8 \u00f7 4) \u00f7 2\u00a0= 2 \u00f7 2\u00a0= 1, but 8 \u00f7 (4 \u00f7 2)\u00a0= 8 \u00f7 2\u00a0= 4.<\/td>\nU+0028\u00a0U+0029<\/th>\n( )<\/th>\n\"(~)\" ( )<\/th>\n<\/tr>\n
parentheses, brackets<\/td>\n<\/tr>\n
everywhere<\/td>\n<\/tr>\n
\n
\u22a2<\/span><\/div>\n<\/td>\n
Turnstile<\/a><\/td>\nx<\/i> \u22a2<\/span> y<\/i> means y<\/i> is provable from x<\/i> (in some specified formal system).<\/td>\nA<\/i> \u2192 B<\/i> \u22a2<\/span> \u00acB<\/i> \u2192 \u00acA<\/i><\/td>\nU+22A2<\/th>\n&#8866;<\/th>\n\"\\vdash\"\\vdash<\/th>\n<\/tr>\n
provable<\/td>\n<\/tr>\n
propositional logic<\/a>, first-order logic<\/a><\/td>\n<\/tr>\n
\n
\u22a8<\/div>\n<\/td>\n
double turnstile<\/a><\/td>\nx<\/i> \u22a8 y<\/i> means x<\/i> semantically entails y<\/i><\/td>\nA<\/i> \u2192 B<\/i> \u22a8 \u00acB<\/i> \u2192 \u00acA<\/i><\/td>\nU+22A8<\/th>\n&#8872;<\/th>\n\"\\vDash\"\\vDash<\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Basic logic symbols Symbol Name Explanation Examples Unicode Value HTML Name LaTeX symbol Read as Category \u21d2 \u2192 \u2283 material implication A \u21d2 B is true only in the case that either A is false or B is true. \u2192 may mean the same as \u21d2 (the symbol may also indicate the domain and codomain…<\/p>\n

Read more →<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[63],"class_list":["post-1264","post","type-post","status-publish","format-standard","hentry","category-bez-kategorii","tag-logika"],"_links":{"self":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts\/1264","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/comments?post=1264"}],"version-history":[{"count":0,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/posts\/1264\/revisions"}],"wp:attachment":[{"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/media?parent=1264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/categories?post=1264"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/u239160.webh.me\/jakisproblem.pl\/index.php\/wp-json\/wp\/v2\/tags?post=1264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}