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authorRossTheRoss <mstrapp@protonmail.com>2021-03-12 08:17:06 -0600
committerRossTheRoss <mstrapp@protonmail.com>2021-03-12 08:17:06 -0600
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add AI hw
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+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)
+
+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.
+
+ 5. No.
+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 \ No newline at end of file