$S$ is a set of arithmetic expressions recursively defined as follows.

Base case: Every variable from the set $\{a,b,c,d,e,f\}$ is in $S.$

Recursive rules: If xinS and yinS, then:

$1.(x+y)inS$

$2.x*yinS$

Indicate which expressions are in $S.$

$(a+b)*c*d$

$(a+(b*c))$

$a*b$

$a*b*c$