A set $S$ together with partial order $\ll$ is called a well order if it has no infinite descending chains, i.e. there is no infinite sequence $x_1, x_2,\ldots$ of elements from $S$ such that $x_{i+1} \ll x_i$ and $x_{i+1} \neq x_i$ for all $i$.
Consider the set of all words (finite sequence of letters $a - z$), denoted by $W$, in dictionary order.
Answer -> E)well order
Minimal Element is 'a', it is less than all elements !
a) False, after aa, we can have ab. Then aba,abb,abc.. Not limited to 24
b) False. after aa, we can have ab,aba,abc.. In fact ab(a-z)*. Not limited to 2^{24}
C)False. Why not partial order ? Dictionary order is partial order ! It is Reflexive, Antysymmetric & Transitive. Even defination of wikipedia says it is !
D) False.Dictionary order is well order .
Defination of Dictionary order -> Ref -> https://en.wikipedia.org/wiki/Lexicographical_order
Given two partially ordered sets A and B, the lexicographical order on the Cartesian product A × B is defined as
3140 Points
1606 Points
1580 Points
1316 Points
1230 Points
1020 Points
1012 Points
970 Points
796 Points
658 Points
232 Points
106 Points
96 Points
63 Points
Gatecse