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).

Write a program that uses a widgetviewer object to do the following: generate two random integers between 1 and 9 (inclusive). name one of them x, the other y. display them to the user using jlabel objects. create a jlabel object displaying the text "enter an operation number." create a jtextfield for the user's input. create a jbutton displaying the text "press here when you've entered your operation." use addandwait to add it to the widgetviewer object. when the user clicks the jbutton, evaluate operation in the following order to determine the one and only mathematical operation to perform on x and y. use a jlabel to display the result. if operation is between 1 and 10 inclusive, add x and y. if operation is evenly divisible by 4, subtract y from x. if operation is evenly divisible by 5, use integer division to divide y into x. if operation is an even number, use floating point division to divide y into x. if none of the other tests on operation apply, multiply x and y. note: operation can be negative or zero.

If the polar bear were taken out of the food chain what would happen to the seal population the seal population would diminish the seal population would grow dramatically the seal population would stay the same the seal population would decrease slightly

Jason works as an accountant in a department store. he needs to keep a daily record of all the invoices issued by the store. which file naming convention would him the most?