1. Prove that the set of all decimal numbers in the interval…

1. Prove that the set of all decimal numbers in the interval (0,1) that end in a string of zeros is countably infinite. (10  points) 2. Is the subset relation A R B if A is a subset of B, a partial order on the Powerset of a given set S? Is it a total order? Give reasons for your answer.  (10 points)

1. Prove that the set of all decimal numbers in the interval…

1. Prove that the set of all decimal numbers in the interval (0,1) that end in a string of zeros is countably infinite. (10  points) 2. Is the subset relation A R B if A is a subset of B, a partial order on the Powerset of a given set S? Is it a total order? Give reasons for your answer.  (10 points)

1. Prove that the set of all decimal numbers in the interval…

1. Prove that the set of all decimal numbers in the interval (0,1) that end in a string of zeros is countably infinite. (10  points) 2. Is the subset relation A R B if A is a subset of B, a partial order on the Powerset of a given set S? Is it a total order? Give reasons for your answer.  (10 points)