For the universal set U= {0,1,2,3,4,5,6,7}
And the sets A={1,5}, B={1,2,3,4}
And C= {4, 6} lists the elements in the following
Sets.
a. A �¿ B
b. A U B�f
c. A �¿(B U C)
d. C �¿ (B �¿ A)�f
I assume your funny symbol is "∩", the intersection symbol
U means: state all elements that you find in either one set OR the other
∩ means: state all elements that you find in both one set AND the other
so let's do c)
A ∩ (B U C)
= A ∩ {1,2,3,4,6}
= {1,5} ∩ {1,2,3,4,6}
={1}
follow this format, the rest are just as easy.
Do i have a correct. {1, 5}
I do not get D. can you explain it to me?
Yes, for c) the correct answer is {1}.
Now, let's move on to d) C ∩ (B ∩ A). In this case, we are finding the intersection of C and the intersection of B and A.
C = {4, 6}
B ∩ A = {1, 5} ∩ {1, 2, 3, 4}
To find the intersection, we need to identify the elements that are present in both sets.
Comparing {1, 5} with {1, 2, 3, 4}, we can see that the only common element is 1.
So, C ∩ (B ∩ A) = {4, 6} ∩ {1} = {}
Therefore, the answer to d) is an empty set {}. This means that there are no elements common between the sets C and the intersection of B and A.