Consider the Kripke structure defined in problem $1,$ and let us call it K$1=($S$,$S$0,$R$1,$L$1).$

Next, consider that we had a second copy of that Kripke structure and lets call it K$2=($T$,$T$0,$R$2,$L$2)$

where T contains states t$0,$ t$1,...,$ t$10,$ and L$2$ contains a similar labeling function with predicates q$0,$ q$1,$

$...,$ q$10.$

Answer the following questions:

a$.$ How many transitions exist in K$1?$

b$.$ Given a synchronous composition of K$1$ and K$2,$ how many states are there? $($Note: You do not

need to analyze whether the states in the composition are reachable.$)$

c$.$ Given an asynchronous composition of K$1$ and K$2,$ how many states are there? $($Note: You do not

need to analyze whether the states in the composition are reachable.$)$

d$.$ Given a synchronous composition of K$1$ and K$2,$ how many predicates are there? $($Note: Use as few

predicates as possible.$)$

e$.$ Given an asynchronous composition of K$1$ and K$2,$ how many predicates are there?

f$.$ Given a synchronous composition of K$1$ and K$2,$ give an upper bound estimate on the number of

transitions?

g$.$ Given an asynchronous composition of K$1$ and K$2,$ give an upper bound estimate on the number of

transitions?