Propose three synthetic routes to t-butyl methyl ether, one each involving
(a) Electrophilic addition reaction
(b) `S_(N)1` reaction
(c ) `S_(N)2` reaction

Explanation

`(CH_(3))_(2)C=CH_(2)+CH_(3)OHoverset(H^(+))rarr(CH_(3))_(3)C-O-CH_(3)`
`(CH_(3))_(2)C=CH_(2)overset(H^(+))rarr(CH_(3))_(3)C^(+)overset(CH_(3)underset(..)overset(..)OH)rarrunderset((CH_(3))_(3)C-O-CH_(3))underset(darr-H^(+))((CH_(3))_(3)C-underset(H)overset(+)O-CH_(3)`
(b) `(CH_(3))_(3)C-Cl+CH_(3)OHrarr(CH_(3))_(3)C-OCH_(3)+HCl`

(c ) `(CH_(3))_(3)COHunderset(CH_(3)Br)overset(Na)rarr(CH_(3))_(3)COCH_(3)`
`(CH_(3))_(3)COH+Nararr(CH_(3))_(3)CO^(-)Na^(+)+(1)/(2)H_(2)uarr`
`(CH_(3))_(3)CO^(-)+CH_(3)Brrarr(CH_(3))_(3)CO-CH_(3)+Br^(-)`