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+# Logic
+
+TODO Manger at lave en summary.
+
+## Opgaver
+
+### 1.
+
+A) Yes, T
+B) Yes, T
+C) Yes, T
+D) Yes, T
+E) No
+F) No
+
+### UNKNOWN ORIGIN (12.)
+
+A) if you have the flu, you miss the final examination
+B) you pass the course if and only if you do not miss the final examination
+C) if you miss the final examination, you do not pass the course
+D) you have the flu, miss the final examination and pass the couse
+
+### 15. (13.)
+
+A) ¬p
+B) p ^ ¬q
+C) p -> q
+D) ¬p -> ¬q
+E) p -> q
+F) q ^ ¬p
+G) q -> p
+
+### 20. (18.)
+
+A) T
+B) T
+C) F
+D) T
+
+### UNKNOWN ORIGIN(31.)
+
+A)
+
+| p  | ¬p | p  ^ ¬p |
+| -- | -- | --      |
+| T  | F  | F       |
+| F  | T  | F       |
+
+B)
+
+| p  | ¬p | p v ¬p |
+| -- | -- | --     |
+| T  | F  | T      |
+| F  | T  | T      |
+
+C)
+
+| p  | q  | p v ¬q | ( p v ¬q) -> q |
+| -- | -- | --     | --             |
+| T  | T  | T      | T              |
+| T  | F  | T      | F              |
+| F  | T  | F      | T              |
+| F  | F  | T      | F              |
+
+D)
+
+| p  | q  | ( p v q) -> ( p ^ q ) |
+| -- | -- | --                    |
+| T  | T  | T -> T = T            |
+| T  | F  | T -> F = F            |
+| F  | T  | T -> F = F            |
+| F  | F  | F -> F = T            |
+
+E)
+
+| p  | q  | (p -> q) | (¬q -> ¬p) | (p -> q) <-> (¬q -> ¬p ) |
+| -- | -- | --       | --         | --                       |
+| T  | T  | T        | T          | T                        |
+| T  | F  | F        | F          | T                        |
+| F  | T  | T        | T          | T                        |
+| F  | F  | T        | T          | T                        |
+
+F)
+
+| p  | q  | (p -> q) | ( q -> p ) | (p -> q) -> ( q -> p) |
+| -- | -- | --       | --         | --                    |
+| T  | T  | T        | T          | T                     |
+| T  | F  | F        | T          | T                     |
+| F  | T  | T        | F          | F                     |
+| F  | F  | T        | T          | T                     |
+
+
+### (40. )
+
+All the paranterees must be true, they can be split up.
+
+r is in two parantesees ( q v ¬r ) and ( r v ¬p ).
+
+If r is true q must also be true for ( q v ¬p ).
+
+Therefore in ( p v ¬p ) p must also be true.
+
+Therefore it creates a kind of circle, that also works then one is false.
+
+### (44. )
+
+A) 
+
+ 01011
+ 11011
+v-----
+ 11011
+ 11000
+^-----
+ 11000
+
+B)
+
+ 01111
+ 10101
+^-----
+ 00101
+ 01000
+v-----
+ 01101
+
+C)
+
+ 01010
+ 11011
+x-----
+ 10001
+ 01000
+x-----
+ 11001
+
+D)
+
+ 11011
+ 01010
+v-----
+ 11011
+
+ 10001
+ 11011
+v-----
+ 11011
+
+ 11011
+ 11011
+^-----
+ 11011
+
+
+### (7. )
+
+Already done this
+
+### (9. )
+
+The rest is just stupid.
+
+### (20. )
+
+| p  | q  | p x q | p <-> q |
+| -- | -- | --    | --      |
+| T  | T  | F     | T       |
+| T  | F  | T     | F       |
+| F  | T  | T     | F       |
+| F  | F  | F     | T       |
+
+The two last columns are the negatives of each other thus
+
+p x q = p <-> q
+
+
+