diff options
Diffstat (limited to 'sem3/BfCI')
| -rw-r--r-- | sem3/BfCI/husk.txt | 14 | ||||
| -rw-r--r-- | sem3/BfCI/mm1.md | 177 | ||||
| -rw-r--r-- | sem3/BfCI/mm3.md | 19 |
3 files changed, 210 insertions, 0 deletions
diff --git a/sem3/BfCI/husk.txt b/sem3/BfCI/husk.txt new file mode 100644 index 0000000..e5a7b96 --- /dev/null +++ b/sem3/BfCI/husk.txt @@ -0,0 +1,14 @@ + + +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/sem3/BfCI/mm1.md b/sem3/BfCI/mm1.md new file mode 100644 index 0000000..933086c --- /dev/null +++ b/sem3/BfCI/mm1.md @@ -0,0 +1,177 @@ +# 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/sem3/BfCI/mm3.md b/sem3/BfCI/mm3.md new file mode 100644 index 0000000..a0bb1b8 --- /dev/null +++ b/sem3/BfCI/mm3.md @@ -0,0 +1,19 @@ +# 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 |