PRELIM: Abstract Algebra

Which of the following are examples of sets?

• The collection of all days in a week beginning with the letter T
• The collection of difficult questions in mathematics
• The collection of active personnel in a company
• The collection of beautiful flowers in the garden

Given the sets A = {3, 5, 7, 9}, B ={2, 4, 6, 8, 10}, C = { 12, 14, 18, 20, 24} and D = {21, 26, 31, 36} Which of the following is true? i. 13 ∈C iii. 36∉D 31 ∈D iv. 4 ∈B

• a. i and ii only
• b. ii and iii only
• c. iii and iv only
• d. ii and iv only

Given the sets A = {3, 5, 7, 9}, B ={2, 4, 6, 8, 10}, C = { 12, 14, 18, 20, 24} and D = {21, 26, 31, 36} The rooster form of set A = {the set of all even numbers less than 12} is ___.

• A = {2, 4, 6, 8, 10, 12}
• A = {0, 2, 4, 6, 8, 10}
• A = { 2, 4, 6, 8, 10}
• A = {2, 4, 6, 8}

Write C = {A, I, C, L, N, P, R} in set builder form.

• C = {the set of letters in the word CALIPER}
• C = {the set of letters in the word CANPLIR}
• C= {set of letters in the word PRINCIPAL}
• C = {set of letters in the word PRINCIPLE}

The set D = { } can be written in set builder form as ____

• D = {x:x ∈N and x>1}
• D = {x:x ∈W}
• D={x:x ∈R}
• none of these

Which set(s) is/are finite? A = { x:x∈N and x is even}, B = {x:x ∈N and x is composite}, C = {the set of letters in the english Alphabet} D = {the set of persons living in a house}

• A and B
• C and D
• B and C
• A and D

Which set(s) is/are infinite? A = { x:x∈N and x is even}, B = {x:x ∈N and x is composite}, C = {the set of letters in the english Alphabet} D = {the set of persons living in a house}

• A and B
• C and D
• B and C
• A and D

The element of set B = {the set of all prime numbers greater than 1 but less than 29} can be listed as ___.

• B = { 1, 3, 5, 7, 11, 13,17, 19, 23}
• B = { 3, 5, 7, 9, 13, 19, 23, 29}
• B = { 2, 3, 5, 7, 11, 13, 17, 19, 23}
• B = {1, 3, 5, 7, 13, 19, 23, 29}

Find the elements of A?

• a. {1, 2, 5, 7}
• b. {1, 7}
• c. {3, 4, 6, 9}
• d. { 2, 8}

What are the elements of B?

• a. {1, 2, 5, 7, 8}
• b. {1, 7}
• c. {3, 4, 6, 9}
• d. { 2, 8}