Post-class 04/03

1 files changed, 30 insertions, 0 deletions

diff --git a/1.3.md b/1.3.md
index a46f0e4..86af4e4 100644
--- a/1.3.md
+++ b/1.3.md
@@ -99,3 +99,33 @@ Truth Table:
 	- with a truth table
 	- by (3)
 3. Use table of Common Equivalences (see link above)
+
+---
+
+# Using the Table of Common Equivalences
+
+- Ex. Show `(p^q)->(p->q)` is a tautology without a truth table
+	- We are goint to solve this using a proof
+	- **Goal**: `(p^q)->(p->q)≡T`
+
+|Proof: (p^q)->(p->q)|Reason|
+|--------------------|------|
+|≡(p^q)->(┓p∨q)      |Implication|
+|≡┓(p^q)∨(┓p∨q)      |Implication|
+|≡(┓p∨┓q)∨(┓p∨q)     |De Morgan|
+|≡┓p∨(┓q∨(┓p∨q))     |Associative|
+|≡┓p∨(┓q∨(q∨┓p))     |Commutative|
+|≡┓p∨((┓q∨q)∨┓p))    |Associative|
+|≡┓p∨(T∨┓p))         |Negation|
+|≡┓p∨T               |Domination|
+|≡T                  |Domination|
+
+- Why use this method?
+	- This method is useful for compound propositions with many propositions
+
+- `n` propositions -> truth table has 2^n rows
+	- e.g 5 propositions -> truth table has 32 rows (!)
+
+---
+
+[1.4 ->](1.4.md)