Given these sets:
A = {3, 4, 5, 6, 7}
B = {6, 7, 8, 9}
C = {2, 4, 6, 8}
List the elements of this set
A(B�¿C)
Show work, step by step.
To find the elements of the set A(B�¿C), follow these steps:
Step 1: Combine sets B and C by taking all elements from both sets without repetition.
B�¿C = {6, 7, 8, 9} ∪ {2, 4, 6, 8}
= {2, 4, 6, 8, 9}
Step 2: Multiply the resulting set (B�¿C) with set A by comparing each element from set A with each element from set (B�¿C).
A(B�¿C) = {3, 4, 5, 6, 7} × {2, 4, 6, 8, 9}
Step 3: Perform the multiplication by comparing each element from set A with each element from set (B�¿C) and taking the set of common values.
For example, let's compare the first element of set A (3) with each element from set (B�¿C).
3 is not in {2, 4, 6, 8, 9} (B�¿C)
Now, let's compare the second element of set A (4) with each element from set (B�¿C).
4 is in {2, 4, 6, 8, 9} (B�¿C)
Similarly, compare each element from set A with each element from set (B�¿C):
5 is not in {2, 4, 6, 8, 9} (B�¿C)
6 is in {2, 4, 6, 8, 9} (B�¿C)
7 is not in {2, 4, 6, 8, 9} (B�¿C)
Step 4: Collect all the common values obtained from the comparison.
A(B�¿C) = {4, 6}
Therefore, the elements of the set A(B�¿C) are {4, 6}.