Proving Implications, Contrapositives, and Biconditionals using Truth Tables
In this lesson, we use truth tables to take a number of biconditionals (if and only ifs) and prove they are logical equivalences. This includes coming up with four different logical equivalences to the implication and a proof showing that the implication proposition is transitive.
Timestamps
00:00 | Intro
00:10 | Review of Implication Logic Operation
01:59 | Review of Logical Equivalence
04:23 | Proving (p→q) ≡ ~(p ^ ~q)
09:38 | Proving (p→q) ≡ (~p v q)
12:09 | Proving the Contrapositive (p→q) ≡ (~q → ~p)
15:26 | Proving the Transitive for the Implication Proposition
20:14 | Proving (p→q) ^ (q→p) ≡ (p ↔ q)
Hashtags
#implication #equivalence #truthtable
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