Given A = {1, 2, 3}, B = {3, 4, 5, 6,}, and C = {3, 5, 7}. Evaluate each set
a) A ∩ B
b) A U C
c) B U C
d) (A U B) ∩ C
e) A U (B U C)
f) (A ∩ B) ∩ C
g) (A ∩ B) U C
a) 3 is the only element in both
b) 1,2,3,5,7 are in one or the other
c) 3,5
d) 1,2,3,4,5,6 intersects 3,5,7 at 3,5
e)everything from 1 to 7 is in at least one set
f) 3 is the only element in A intersects B. 3 is also in C so the answer is 3.
g) 3, 5, 7
thanks Damon, i understand it a little better now :)
To evaluate each set, we will use the following set operations:
1. Union (∪): The union of two sets A and B is the set that contains all elements that are in A or B (or both).
2. Intersection (∩): The intersection of two sets A and B is the set that contains all elements that are in both A and B.
Let's evaluate each set step by step:
a) A ∩ B:
To find the intersection of sets A and B, we look for elements that are common to both sets.
A = {1, 2, 3}
B = {3, 4, 5, 6}
So, A ∩ B = {3}.
b) A U C:
To find the union of sets A and C, we combine all the elements from both sets without duplicating any elements.
A = {1, 2, 3}
C = {3, 5, 7}
So, A U C = {1, 2, 3, 5, 7}.
c) B U C:
To find the union of sets B and C, we combine all the elements from both sets without duplicating any elements.
B = {3, 4, 5, 6}
C = {3, 5, 7}
So, B U C = {3, 4, 5, 6, 7}.
d) (A U B) ∩ C:
To evaluate this expression, we first find the union of sets A and B, and then find the intersection with set C.
A = {1, 2, 3}
B = {3, 4, 5, 6}
C = {3, 5, 7}
A U B = {1, 2, 3, 4, 5, 6}
(A U B) ∩ C = {3, 5}
e) A U (B U C):
To evaluate this expression, we first find the union of sets B and C, and then find the union with set A.
A = {1, 2, 3}
B = {3, 4, 5, 6}
C = {3, 5, 7}
B U C = {3, 4, 5, 6, 7}
A U (B U C) = {1, 2, 3, 4, 5, 6, 7}
f) (A ∩ B) ∩ C:
To evaluate this expression, we find the intersection of sets A and B, and then find the intersection with set C.
A = {1, 2, 3}
B = {3, 4, 5, 6}
C = {3, 5, 7}
A ∩ B = {3}
(A ∩ B) ∩ C = {3}
g) (A ∩ B) U C:
To evaluate this expression, we first find the intersection of sets A and B, and then find the union with set C.
A = {1, 2, 3}
B = {3, 4, 5, 6}
C = {3, 5, 7}
A ∩ B = {3}
(A ∩ B) U C = {3, 5, 7}
So, the evaluated sets are:
a) A ∩ B = {3}
b) A U C = {1, 2, 3, 5, 7}
c) B U C = {3, 4, 5, 6, 7}
d) (A U B) ∩ C = {3, 5}
e) A U (B U C) = {1, 2, 3, 4, 5, 6, 7}
f) (A ∩ B) ∩ C = {3}
g) (A ∩ B) U C = {3, 5, 7}