3 Let

be the relation of reduction:

L_(0)

if there is a polynomial-time reduction

\\\ ho :(0+1)^(**)->

0+1

such that\

AA\\\\sigma in(0+1)^(**):[\\\\sigma inL_(0)Longleftrightarrow\\\\sigma inL_(1)]

\ Show that the

relation is a transitive relation on languages. That is, show that if

L_(1)

and

L_(2)

, then

L_(1)

.

3 Let P be the relation of reduction: L0PL1 if there is a polynomial-time reduction :(0+1) 0+1) such that (0+1):[L0L1] Show that the P relation is a transitive relation on languages. That is, show that if L1PL2 and L2PL3, then L1PL3