A compound A with a molecular formula $C_5{H}_{10}O$ gives the following results:

a$),A+2,4-DNP$ : positive

b$)A+$ Tollens' test : negative

c$)A+NaB{H}_4$ gives $B$

d$)Bx+$ concentrated $H_{2}S{O}_4$ gives $C(C_5{H}_{10})$

e$)C+O_{3}D+E(C_3{H}_{6}O)$

Compound D gives positive result with Tollens' reagent while $E$ gives otherwise. However, both give positive results with iodoform test. Give the structures of A$,$ B$,$ C and $D.$