Condition of inclusion for $(a,b) \subset (c,d)$ , $[a,b] \subset (c,d)$ , $(a,b) \subset [c,d)$?

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(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 ?