From 7a73162607544204032aa66cce755daf21edebda Mon Sep 17 00:00:00 2001
From: Matt Strapp <matt@mattstrapp.net>
Date: Tue, 24 May 2022 11:18:46 -0500
Subject: Graduate

Signed-off-by: Matt Strapp <matt@mattstrapp.net>
---
 csci4511w/hw3.txt | 94 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 94 insertions(+)
 create mode 100644 csci4511w/hw3.txt

(limited to 'csci4511w/hw3.txt')

diff --git a/csci4511w/hw3.txt b/csci4511w/hw3.txt
new file mode 100644
index 0000000..37af197
--- /dev/null
+++ b/csci4511w/hw3.txt
@@ -0,0 +1,94 @@
+1)
+	1. Valid (it is always true)
+	2. Neither (this is occasionally true)
+	3. Neither
+		A⇒B (C)	~A⇒~B (D)	C⇒D
+		T		T			T
+		F		T			T
+		T		F			F
+		T		T			T
+		
+	4. Valid (A v ~A is always true)
+	5. Neither
+		A	B	C	A⇒B (D)	B⇒C	(E)	D⇒E	
+		T	T	T	T		T		T
+		T	T	F	T		F		F
+		T	F	T	F		T		T
+		T	F	F	F		T		T
+		F	T	T	T		T		T
+		F	T	F	T		F		F
+		F	F	T	T		T		T
+		F	F	F	T		T		T
+	6. Valid
+		(A⇒B)⇒((~A|~C)⇒B)
+		A	B	C	A⇒B (D)	((~A|~C)⇒B)	(E)	D⇒E	
+		T	T	T	T		T				T
+		T	T	F	T		T				T
+		T	F	T	F		F				T
+		T	F	F	F		T				T
+		F	T	T	T		T				T
+		F	T	F	T		T				T
+		F	F	T	T		T				T
+		F	F	F	T		T				T
+	7. Valid (at least one is always true)
+		A	B	A⇒B
+		T	T	T			
+		T	F	F
+		F	T	T
+		F	F	T
+	8. Neither
+		A	B	A^B (C)	C∨~B
+		T	T	T		T
+		T	F	F		T
+		F	T	F		F
+		F	F	F		T
+	9. Valid
+		A	B	C	(P⇒Q)∧(Q⇒R)	(D)	D⇒(A⇒C)
+		T	T	T	T				T
+		T	T	F	T				T
+		T	F	T	F				T
+		T	F	F	T				T
+		F	T	T	F				T
+		F	T	F	F				T
+		F	F	T	F				T
+		F	F	F	T				T
+	10. Valid (this truth table is really long but it turns out to be a tautology)
+
+2) (A^B)⇒C == (~A∨~B)⇒C
+	1. They are both true iff all 3 are true so no?
+	2. Yes. This is the statement.
+	3. No. AND and OR are not interchangable.
+	4. No.
+		"If the night is quiet, then both the dog sleeps and the house is warm"
+	5. No.
+		"The dog does not sleep or the night is not quiet or the house is warm"
+
+3)
+	1. ~~(~C∨~D)∨P
+		-> ~C∨~D∨P
+	2. ~J∨(Wi^We)
+		-> (~J∨Wi) [a]^(~J∨We) [b]
+	3. ~Wi∨D
+	4. ~We∨C
+	5. J
+	--REFUTATION--
+	6. ~P
+	7. (1,6) ~C∨~D
+	8. (7,3) ~Wi∨~C
+	9. (8,4) ~Wi∨~We
+   10. (9,2a) ~J∨~We
+   11. (10,5) ~We
+   12. (11,2b) ~J
+   13. (5,12) NIL
+
+4)
+	1. A∨B∨C
+	2. ~A∨B
+	3. ~B [a]^ ~D [b]
+	4. ~C∨D
+	--REFUTATION--
+	5. (1,4) A∨B∨D
+	6. (3,5) A∨D
+	7. (6,4) A
+	8. (7,2) B
+	9. (8,3) NIL
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