Can Mathematica 9 convert a Boolean representation of an RBD to its symbolic algebraic form?

If I have a simple series configuration made up of 2 components

bexpr1=And[c1,c2]

and the corresponding symbolic representation for the system would be RS1 = R1*R2

The system I am interested in is more complex and contains 7 components in a 4 path architecture:

path1=And[c1,c2,c5,c7]

path2=And[c1,c3,c5,c7]

path3=And[c1,c3,c6,c7]

path4=And[c1,c4,c6,c7]

bexpr2=Or[path1,path2,path3,path4]

Of course, other systems can have higher complexity.

How can the algebraic form of the reliability function be obtained for bexpr2?

Thank you.