;
;
;
;
,
and so on. Then 
Æ,
,
and A and B does not contain any arithmetic progression, since for any
arithmetic progression 
,
both sets contains of blocks of lengths exceeding b.Solution :
Yes. For example, say
;
;
;
;
,
and so on. Then Æ,
,
and A and B does not contain any arithmetic progression, since for any
arithmetic progression ,
both sets contains of blocks of lengths exceeding b.