3. In IT department, the students supposed to study three courses from Math section that is Calculus I, Mathematics for IT and Discrete Structure. The academic plan requires to complete prerequisites courses to proceed with the next courses that are based on as shown on table 1. Clearly, if student is studying Mathematics for IT then student studied (passed) Calculus I and if student is studying Discrete Structure then student studied (passed) Calculus I and Mathematics for IT. A new advisor (Nasser) joined the department and needs to know what are the courses that the advisees studied. However, he is only provided by their courses for current semester in table 1. Answer the following Course Code Course Name Prerequisites None MATH1200 Calculus I Level Diploma Diploma Advance Diploma MATH201 Mathematics for IT Calculus I MATH2200 Discrete Structure Calculus I and Mathematics for IT Table 1: Courses' Information Student Name Current Registered Course Asma Calculus I Wafa Discrete Structure Sana Discrete Structure Anas Mathematics For IT Younis Discrete Structure Shefa Calculus I Ali Calculus I Amgad Mathematics for IT Table 2: Advisees names with current registered Course (a) Write three propositions that constructed from table 1. (Example: p: student study Calculus I, q: student study Mathematics for IT. The proposition: If student studied Calculus I then he will study Mathematics for IT) (b) Let A be a set of students names and B be a set of courses. The relations R₁ and R₂ from A to B such that R₁ = {(a,b): a A,b B, a studied b} and R₂ = {(a,b): a A, b E B, a is studying b}. Find the following using table 2: (a) R₁ and R₂ (b) Are R₁ and R₂ disjoint sets? Explain. (c) Let R3 be the advised courses for next semester if student passed current course. Find R3. (d) Prove and explain that R₂ R3 = R₂U R3.
3. In IT department, the students supposed to study three courses from Math section that is Calculus I, Mathematics for IT and Discrete Structure. The academic plan requires to complete prerequisites courses to proceed with the next courses that are based on as shown on table 1. Clearly, if student is studying Mathematics for IT then student studied (passed) Calculus I and if student is studying Discrete Structure then student studied (passed) Calculus I and Mathematics for IT. A new advisor (Nasser) joined the department and needs to know what are the courses that the advisees studied. However, he is only provided by their courses for current semester in table 1. Answer the following Course Code Course Name Prerequisites None MATH1200 Calculus I Level Diploma Diploma Advance Diploma MATH201 Mathematics for IT Calculus I MATH2200 Discrete Structure Calculus I and Mathematics for IT Table 1: Courses' Information Student Name Current Registered Course Asma Calculus I Wafa Discrete Structure Sana Discrete Structure Anas Mathematics For IT Younis Discrete Structure Shefa Calculus I Ali Calculus I Amgad Mathematics for IT Table 2: Advisees names with current registered Course (a) Write three propositions that constructed from table 1. (Example: p: student study Calculus I, q: student study Mathematics for IT. The proposition: If student studied Calculus I then he will study Mathematics for IT) (b) Let A be a set of students names and B be a set of courses. The relations R₁ and R₂ from A to B such that R₁ = {(a,b): a A,b B, a studied b} and R₂ = {(a,b): a A, b E B, a is studying b}. Find the following using table 2: (a) R₁ and R₂ (b) Are R₁ and R₂ disjoint sets? Explain. (c) Let R3 be the advised courses for next semester if student passed current course. Find R3. (d) Prove and explain that R₂ R3 = R₂U R3.
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Transcribed Image Text:3. In IT department, the students supposed to study three courses from Math section that is Calculus
I, Mathematics for IT and Discrete Structure. The academic plan requires to complete prerequisites
courses to proceed with the next courses that are based on as shown on table 1. Clearly, if student
is studying Mathematics for IT then student studied (passed) Calculus I and if student is studying
Discrete Structure then student studied (passed) Calculus I and Mathematics for IT. A new advisor
(Nasser) joined the department and needs to know what are the courses that the advisees studied.
However, he is only provided by their courses for current semester in table 1.
Answer the following
Course Code
Course Name
Prerequisites
None
MATH1200
Calculus I
Level
Diploma
Diploma
Advance Diploma
MATH201 Mathematics for IT
Calculus I
MATH2200 Discrete Structure Calculus I and Mathematics for IT
Table 1: Courses' Information
Student Name Current Registered Course
Calculus I
Asma
Wafa
Discrete Structure
Sana
Discrete Structure
Anas
Mathematics For IT
Younis
Discrete Structure
Shefa
Calculus I
Ali
Calculus I
Amgad
Mathematics for IT
Table 2: Advisees names with current registered Course
(a) Write three propositions that constructed from table 1. (Example: p: student study Calculus I,
q: student study Mathematics for IT. The proposition: If student studied Calculus I then he will
study Mathematics for IT)
(b) Let A be a set of students names and B be a set of courses. The relations R₁ and R₂ from A to B
such that R₁ = {(a,b): a A,b € B, a studied b} and R₂ = {(a,b): a A,b E B, a is studying b}.
Find the following using table 2:
(a) R₁ and R₂
(b) Are R₁ and R₂ disjoint sets? Explain.
(c) Let R3 be the advised courses for next semester if student passed current course. Find R3.
(d) Prove and explain that R₂ R3 = R₂ U R3.
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