1. Let A = {0, 2, 4, 6, 8}, B = {0, 1, 2, 3, 4}, C = {0, 3, 6, 9}. Find (a) ABC
ID: 3754451 • Letter: 1
Question
1. Let A = {0, 2, 4, 6, 8}, B = {0, 1, 2, 3, 4}, C = {0, 3, 6, 9}. Find
(a) ABC
(b) ABC
(c) (AB)C
(d) A(BC)
(e) (AB)C
2. List the elements of each set and give its cardinality.
A = {x Z + : x is an integer multiple of 3 and x < 16}
3. Define sets A, B and C as follows:
A = {2,4,6,8}
B = {x Z: x is even and 0 < x < 10}
C = {x Z: x is even and 0 < x 10}
Indicate whether each of the following statements is true or false. Justify your answer.
(a) A B
(b) A B
4. Find the power set for set A={a, b, c}
Explanation / Answer
Given A = {0, 2, 4, 6, 8}, B = {0, 1, 2, 3, 4}, C = {0, 3, 6, 9}
(a) ABC
AB = {0, 2, 4, 6, 8} {0, 1, 2, 3, 4} = {0, 1, 2, 3, 4, 6, 8}
ABC = (AB)C = {0, 1, 2, 3, 4, 6, 8}{0, 3, 6, 9} = {0, 1, 2, 3, 4, 6, 8, 9}
(b) ABC
AB = {0, 2, 4, 6, 8} {0, 1, 2, 3, 4} = {0, 2, 4 }
ABC = (AB)C {0, 2, 4 } {0, 3, 6, 9} = {0}
(c) (AB)C
AB = {0, 2, 4, 6, 8} {0, 1, 2, 3, 4} = {0, 1, 2, 3, 4, 6, 8}
(AB)C = {0, 1, 2, 3, 4, 6, 8}{0, 3, 6, 9} = {0, 3, 6}
(d) A(BC)
(BC) = {0, 1, 2, 3, 4}- {0, 3, 6, 9} = {1, 2, 4}
A(BC) = {0, 2, 4, 6, 8} - {1, 2, 4} = {0, 6, 8}
(e) (AB)C
(AB) = {0, 2, 4, 6, 8} - {0, 1, 2, 3, 4} = {6, 8}
(AB)C = {6, 8}- {0, 3, 6, 9} = { 8 }
4) Power Set of A is
Answer: P(A) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} }
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