Let U={u,n,i,t,e}
A={n,i,t}
B={n,e}
C={u,n,i,t,e}
D={u,e}
Find each of the following:
(a)A(with upside down horseshoe)B
(b)C U D
(c)D (with line over the D)
show solution
(a) A intersection B = {n}
(b) C union D = {u,n,i,t,e}=C
(c) complement of D = {n,i,t}=A
how do u get this
To find the solution for each of the following set operations, we need to understand the symbols used.
In the given context:
- Upside down horseshoe (∩) represents the intersection of two sets.
- U represents the universal set, which contains all the elements in consideration.
- Uppercase letters A, B, C, and D represent the given subsets.
Now, let's solve each of the following set operations step by step:
(a) A (∩) B:
To find the intersection of sets A and B, we need to identify the elements common in both sets A and B.
A = {n, i, t}
B = {n, e}
The intersection (∩) of A and B consists of elements that are present in both sets A and B. From the given sets, the common element is "n".
Therefore, A (∩) B = {n}
(b) C U D:
To find the union of sets C and D, we need to combine all the elements from sets C and D, eliminating any duplicate elements.
C = {u, n, i, t, e}
D = {u, e}
The union (U) of sets C and D consists of all the unique elements from both sets. Combining the given sets, we get:
C U D = {u, n, i, t, e}
Therefore, C U D = {u, n, i, t, e}
(c) D̅:
The symbol with a line over D (D̅) represents the complement of set D, which consists of all the elements from the universal set U that are not present in set D.
U = {u, n, i, t, e}
D = {u, e}
The complement (D̅) of set D contains all the elements from the universal set U that are not in D. Hence, we remove the elements "u" and "e" from U. The resulting set is:
D̅ = {n, i, t}
Therefore, D̅ = {n, i, t}
I hope this explanation helps! Let me know if you have any further questions.