Admin at 08:34, 23 May 2014

Admin — Fri, 23 May 2014 08:34:35 GMT

← Older revision		Revision as of 08:34, 23 May 2014
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	* [[wikipedia:Material_conditional\|Material conditional]]		* [[wikipedia:Material_conditional\|Material conditional]]
	* [[wikipedia:If_and_only_if\|If and only if]]		* [[wikipedia:If_and_only_if\|If and only if]]
		+
		+	== Overview ==
		+
		+	===Implication(→)===
		+
		+	"α→β" is "α implies β." or "if α then β."
		+
		+	0 means false, 1 means true, and ≡ means equivalent.
		+
		+	Case of implication. "P→Q" ≡ "￢P∨Q" ≡ "￢(P∧￢Q)"
		+
		+	{\| border="1" class="wikitable" style="background-color:#ddf"
		+	! style="background:#ffdead;" \|　P
		+	! style="background:#ffdead;" \|　Q
		+	! style="background:#ffdead;" \|　P→Q
		+	! style="background:#ffdead;" \|　￢P
		+	! style="background:#ffdead;" \|　￢Q
		+	! style="background:#ffdead;" \|　￢P∨Q
		+	! style="background:#ffdead;" \|　P∧￢Q
		+	! style="background:#ffdead;" \|　￢（P∧￢Q）
		+	\|-
		+	\|　0
		+	\|　0
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|-
		+	\|　0
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|-
		+	\|　1
		+	\|　0
		+	\|　0
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|-
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　0
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|-
		+	\|}
		+
		+
		+	===Equivalence(⇔ or ≡)===
		+
		+	Case of equivalence. "P⇔Q" ≡ "(P→Q)∧(Q→P)"
		+
		+	{\| border="1" class="wikitable" style="background-color:#ddf"
		+	! style="background:#ffdead;" \|　P
		+	! style="background:#ffdead;" \|　Q
		+	! style="background:#ffdead;" \|　P⇔Q
		+	! style="background:#ffdead;" \|　P→Q
		+	! style="background:#ffdead;" \|　Q→P
		+	! style="background:#ffdead;" \|　（P→Q）∧（Q→P）
		+	\|-
		+	\|　0
		+	\|　0
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|-
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|　0
		+	\|-
		+	\|　1
		+	\|　0
		+	\|　0
		+	\|　0
		+	\|　1
		+	\|　0
		+	\|-
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|　1
		+	\|-
		+	\|}
		+

	== CAI Exercise ==		== CAI Exercise ==

Admin: Created page with 'Logic > Implication and equivalence == Contents == * Category:Mathematical logic（Wikipedia） * [[wikipedia:Boolean_algebra_(l…'

Admin — Fri, 23 May 2014 04:23:50 GMT

Created page with 'Logic > Implication and equivalence == Contents == * Category:Mathematical logic（Wikipedia） * [[wikipedia:Boolean_algebra_(l…'

New page

[[Logic]] > Implication and equivalence

== Contents ==

* [[wikipedia:Category:Mathematical logic|Category:Mathematical logic（Wikipedia）]]
* [[wikipedia:Boolean_algebra_(logic)|Boolean algebra (logic)]]
* [[wikipedia:Material_conditional|Material conditional]]
* [[wikipedia:If_and_only_if|If and only if]]

== CAI Exercise ==

*[[cai_en:EDULOG00010006|Go to CAI Exercise page]]

[[en:Logic/Implication and equivalence]]
[[ja:論理学/含意と同値]]

Logic/Implication and equivalence - Revision history

Admin at 08:34, 23 May 2014

Admin: Created page with 'Logic > Implication and equivalence == Contents == * Category:Mathematical logic（Wikipedia） * [[wikipedia:Boolean_algebra_(l…'