Question 1. Using Boolean algebra, prove that:

X'Y + XYZ' + Y' + XZ (Y+Y') = 1

Question 2. University(Uni) has opened an IT Doctorate study in Sydney Study Centre. The applicant should has a master degree in IT or a master degree in electrical engineering. The applicant should also has completed project subject (e.g. ITC570, ITC571, ...)in his master degree. Before Uni management staff approve student's application, they have to check student master degree if it meet the requirements and also check if the student completed project subject or not in his master degree. After checking applicant documents, Uni staff has come to the following conclusions:

Approve if applicant has one of the required master degrees and has completed project subject.

Approve if applicant has two of the required master degrees and has completed project subject.

Don't approve otherwise.

Construct a truth table and find the minimized Boolean function to implement the logic telling the CSU staff when to approve. Draw a circuit diagram for the Boolean function.

Question 3. Complete the truth table for the following sequential circuit: