A. " Every subset of a regular set is regular": False. Regular Languages not closed under subset operation.
Ex: P = $(a+b)*$, Q = ${ a^nb^n, n >0}$
C." The union of two non regular set is not regular": Not necessarily.
False Example: P $= { a^nb^n, n >100}$, Q$ = { a^nb^n, n >0} $P $\bigcup$ Q$ = { a^nb^n, n >100}$ ,
True Example: P$ = { a^nb^n, n<m, m,n>=0}$ Q$ = { a^nb^n, , n>=m, m,n>=0}$, P $\bigcup$ Q$ = { a^mb^n,m,n>=0}$
D. " Infinite union of finite set is regular ": False
In infinite union union operation is done infinite (uncountably many) times.
B. " Every finite subset of non-regular set is regular": True.
Finite language is always regular.
So B is correct.
