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Papers

Paper #1 First Class

Title: Set Theory

Module: Module 1

Class: Quantitative Reasoning

Paper: Case Assignment

Number of Pages: 1

1. Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}.

Determine A ? (B n C)

Solution

To determine A ? (B n C), we first have to find out the intersection between B and C.

(B n C) = {q, s, y, z} n {v, w, x, y, z}

(B n C) = {y, z}

Now, we will find the Union part.

A ? (B n C) = {q, s, u, w, y} ? {y, z}

Result

A ? (B n C) = {q, s, u, w, y, z}

2. Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}

Determine A n (B ? C)

Solution

To determine A n (B ? C), we first have to find out the Union between B and C.

(B ? C) = {q, s, y, z} ? {v, w, x, y, z}

(B ? C) = {q, s, v, w, x, y, z,}

Now,

A n (B ? C) = {q, s, u, w, y} n {q, s, v, w, x, y, z,}

Result

A n (B ? C) = {q, s, w, y}

3. Construct a Venn diagram illustrating the following sets.

3) U = {2, 4, 6, 8, 10, 12}

A = {2, 6, 10}

B = {2, 4, 8}

C = {2, 8, 10, 12}

Solution

4. Find n(A) for the set A = {3, 5, 7, 9, 11}

Solution

The elements of a set are n(A), in set theory, an element or member of a group (or family of sets ) is an object that is part of that set. Therefore, n(A) = 5 for the above mentioned Set A.

5. Find n(A) for the set A = {x | x is a second in a minute}

Solution

The n(A) for the above mention = 60

References

Thomas J. (2009). Introduction to set theory. Dekker Publisher, Pp: 1-109

Johnson, P. (2002). A History of Set Theory. Prindle, Weber & Schmidt, pp. 56-60.

Kunen, K. (2000). Set Theory: An Introduction to Independence Proofs. North-Holland, pp. 100-110.

Tiles, M. (2009). The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. Dover Publications, pp. 45-50.

Paper #2 First Class

Title: Set Theory

Module: Module 1

Class: Quantitative Reasoning

Paper: SLP

Number of Pages: 1

A = {x | x is the list of 5 items I Need to buy the most}

A = {Food, Clothes, Home, Car, Education}

The above mentioned set A, contains the list of all the five items I Need to buy the most.

B = {x | x is the list of 5 items I Want to buy the most}

B = {Mobile, Play station, Laptop, Music Player, Bike}

The above mentioned set B, contains the list of all the five items I Want to buy the most.

A ? B = {Food, Clothes, Home, Car, Education, Mobile, Play station, Laptop, Music Player, Bike}

A n B = {}

Price ...