(4) 1. 2. 3. 4. You are presented with a set of requirements under which a stude
ID: 2249001 • Letter: #
Question
(4) 1. 2. 3. 4. You are presented with a set of requirements under which a student gets admitted to the graduate school at the TT University. The applicant must be: An applicant with 3.0 GPA or over, or A female minority with less than 3.0 GPA, or A male with less than 3.0 GPA and has two years of calculus, or A minority male who has two years of calculus The variables w, x, y, and z assume the truth value 1 in the following cases: w = l if applicant has two years of calculus, x = 1 if applicant is minority y = 1 if applicant is a male; z = l if applicant has less than 3.0 GPA Find a minimum SOP expression which assumes the value 1 whenever the student is admitted to the school of engineering at TT UniversityExplanation / Answer
As per the information available from the question,
& Assuming gender of an applicant is either male or female
The following variables can be defined:
Applicant having two years calculus = w
Applicant NOT having two years calculus = w' (w bar), such that (w + w' = 1) Complement Law of Boolean Algebra
Similarly,
Applicant is minority = x
Applicant is NOT minority = x' (x bar)
Applicant is male = y
Applicant is NOT male (female) = y' (y bar)
Applicant has less than 3 GPA = z
Applicant has NOT less than 3 GPA = z' (z bar)
Now, defining the conditions to be satisfied by applicants for successful admission:
1. Applicant with GPA >= 3.0 ---> z' OR
2. Female = (y'), Minority = (x), GPA < 3 = (z) ---> (y' AND x AND z) OR
3. Male = (y), GPA < 3 = (z), Two Year Calculus = (w) ---> (y AND z AND w) OR
4. Minority = (x), Male = (y), Two Year Calculus ---> (x AND y AND w)
SOP Expression for Admission = z' + y'xz + yzw + xyw
Simplifying this expression (You can do the simplification by K-Map Method as well):
(z' + y'x)*(z' + z) + yzw + xyw
(z' + y'x)*1 + yzw + xyw
z' + y'x + yzw + xyw
z' + yzw + x*(y' + yw)
(z' + yw)*(z' + z) + x'*[(y' + y)*(y' + w)]
z' + yw + x'*(y' + w)
z' + yw + x'y' + x'w
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.