Arrange the following in the increasing order of stability:
$(a) \ CH_3CH=CH-CHO$
$(b) \ CH_3-CH^+-CH=C(O^-)H$
$(c) \ ^+CH_2-CH=CH-CHO$

(C) The stability of resonance structures is determined by the following rules:
$1$. Structures with more covalent bonds are more stable.
$2$. Structures with complete octets for all atoms are more stable.
$3$. Structures with less charge separation are more stable.
$4$. Negative charge on a more electronegative atom and positive charge on a less electronegative atom is more stable.
In structure $(a)$,all atoms have complete octets and there is no charge separation,making it the most stable.
In structure $(b)$,the positive charge is on a carbon atom and the negative charge is on an oxygen atom (more electronegative),which is relatively stable.
In structure $(c)$,the positive charge is on a terminal carbon atom,which is less stable compared to $(b)$ due to the lack of adjacent electron-donating groups or resonance stabilization of the positive charge.
Therefore,the increasing order of stability is $(c) < (b) < (a)$.