(1) $(a,b) \subset (c,d)$
Condition : if $ a<x<b$ then $c<x<d $
Combining both, $c\leq a<x<b \leq d$
(2) $[a,b] \subset (c,d)$
Condition : if $ a\leq x\leq b$ then $c<x<d $
Combining both, $c< a \leq x\leq b< d$
(3) $(a,b) \subset [c,d)$
Condition : if $ a<x<b$ then $c\leq x<d $
Combining both, $c \leq a < x < b \leq d$
Is the last inequality of each expression true ?