diff options
Diffstat (limited to 'sem1/BfCI')
| -rw-r--r-- | sem1/BfCI/husk.txt | 14 | ||||
| -rw-r--r-- | sem1/BfCI/mm1.md | 177 | ||||
| -rw-r--r-- | sem1/BfCI/mm3.md | 19 |
3 files changed, 0 insertions, 210 deletions
diff --git a/sem1/BfCI/husk.txt b/sem1/BfCI/husk.txt deleted file mode 100644 index e5a7b96..0000000 --- a/sem1/BfCI/husk.txt +++ /dev/null @@ -1,14 +0,0 @@ - - -log(log(x^4)) = log(log(x)) - -Husk at 4 flytter sig uden for log(x). - - -x^2-1 = (x-1)(x+1) - -lim(to inf) f(x) over g(x) = { - 0 -> f is O(g) - const -> f(x) = THETA(g(x)) - INF -> f is OMEGA(g) -} diff --git a/sem1/BfCI/mm1.md b/sem1/BfCI/mm1.md deleted file mode 100644 index 933086c..0000000 --- a/sem1/BfCI/mm1.md +++ /dev/null @@ -1,177 +0,0 @@ -# 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 - - - diff --git a/sem1/BfCI/mm3.md b/sem1/BfCI/mm3.md deleted file mode 100644 index a0bb1b8..0000000 --- a/sem1/BfCI/mm3.md +++ /dev/null @@ -1,19 +0,0 @@ -# Lektier - -## Steps til strong induction bevis - -1. *[Basis step]* start med at bevis at P(1) er sandt. Altså hvad resten vil bygge på. -2. *[Inductive step]* bevis at hvis de første P(1 til k) er sandt er P(k+1) også sandt. - -## Recursive function - -En funktion der regner factorial. -Altså f(x) = 1 * 2 * 3 * .. * x - -Her vil f(1) = 1. -Og resten vil være f(x) = x * f(x-1). - -f(1) = 1 -f(2) = 2 * f(1) = 2 * 1 = 2 -f(3) = 3 * f(2) = 3 * 2 = 6 -f(4) = 4 * f(3) = 4 * 6 = 16 |