Biimplikation: Forskelle mellem versioner
Content deleted Content added
Glenn (diskussion | bidrag) m +symbol |
Glenn (diskussion | bidrag) +afsnit fra https://en.wikipedia.org/w/index.php?title=If_and_only_if&oldid=1117279147#Definition og tilpasset |
||
Linje 6:
Operanderne P og Q siges at være ''ækvivalente'' (eller logisk ækvivalente); i matematikken betyder det at operanderne udtrykker det samme [[fænomen]] på forskellige måder.
==Definition==
[[Sandhedstabellen]] for ''P'' <math>\Leftrightarrow</math> ''Q'' er som følger - sidste søjle:<ref>[http://www.wolframalpha.com/input/?i=p+%3C%3D%3E+q p <=> q]. [[Wolfram Alpha|Wolfram|Alpha]]</ref><ref>{{citation |title=If and only if |publisher=UHM Department of Mathematics |url=http://www.math.hawaii.edu/~ramsey/Logic/Iff.html |quote=Theorems which have the form "P if and only Q" are much prized in mathematics. They give what are called "necessary and sufficient" conditions, and give completely equivalent and hopefully interesting new ways to say exactly the same thing.}}</ref>
{| class="wikitable" style="margin:1em auto; text-align:center; float:left"
|+ Sandhedstabel
|-
! scope="col" style="width:20%" | ''P''
! scope="col" style="width:20%" | ''Q''
! scope="col" style="width:20%" | {{nowrap|''P'' <math>\Leftrightarrow</math> ''Q''}}
|-
| S || S || S
|-
| S || style="background:papayawhip" | F || style="background:papayawhip" | F
|-
| style="background:papayawhip" | F || S || style="background:papayawhip" | F
|-
| style="background:papayawhip" | F || style="background:papayawhip" | F || S
|}
{{clear}}
Sandhedstabellen for ''P'' <math>\Leftrightarrow</math> ''Q'' er ækvivalent med det som produceres af en [[XNOR-gate]] (NOT af en [[XOR-gate]]) - og det modsatte af hvad der produceres af en [[XOR-gate]].<ref>{{Cite web|url=http://www.cburch.com/logisim/docs/2.1.0/libs/gates/xor.html|title=XOR/XNOR/Odd Parity/Even Parity Gate|website=www.cburch.com|access-date=2019-10-22}}</ref>
== Biimplikation i matematik ==
| |||