Please solve the following problems based on the definitions in my lecture on orders and trees:1. Draw the following Poset. (25 points)a. Set S: divisors of 60b. Relation R (denoted ‘<’): x < y iff x is a proper divisor of yi. x is a proper divisor of y iff x divides y and x  y 2. Prove that a partial order cannot be symmetric. (25 points)3. Give an example of an infinite tree of depth 3. (50 points)Your examples in Problem 3 should be formalized as a Poset. That is, you must precisely specify a set S and a relation R defined over S such that the visual representation of R would be a tree that meets the required properties. For example, for Problem 3, you should specify a Poset (S, R) such that the depth of its tree representation cannot go beyond 3 (starting from the root).