Answer to Question #294617 in Discrete Mathematics for Yaku

Question

In the grammar of natural languages, such as Sesotho, noun words are categorised into equivalent noun classes, based on their generating “stems”. A stem is a noun word prefix, which is the “first syllable” of the noun word, from where suffixes could be attached to generate different noun words. In Sesotho, in particular, the equivalence noun classes are based on the following two relations:

R₁: A noun word x is related to another noun word y iff x and y have the same stem

R₂: A noun word x is related to another noun word y iff x and y have no stems. R₂

generates the equivalence Class 9.

a) Prove that:

i) R₁ is an equivalence relation

ii) R₂ is also an equivalence relation

b)

i) List any three (3) noun words belonging to Class 9

ii) Show that “se” is a stem by showing that C(“sekatana”) is an equivalence class by listing any first eleven (11) words in it.