If A = {x, y, z} and B = {u, v, w, x}, and the universe is {s, t, u, v, w, x,…
2020
If A = {x, y, z} and B = {u, v, w, x}, and the universe is {s, t, u, v, w, x, y, z}. Then (A U B') ∩ (A ∩ B) is equal to
- A.
{u, v, w, x}
- B.
{x}
- C.
{u, v, w, x, y, z}
- D.
{u, v, w}
Attempted by 113 students.
Show answer & explanation
Correct answer: B
Solution:
Given:
A = {x, y, z}
B = {u, v, w, x}
Universe U = {s, t, u, v, w, x, y, z}
Step 1: Find B'
B' = U - B
B' = {s, t, y, z}
Step 2: Find A ∪ B'
A ∪ B' = {x, y, z} ∪ {s, t, y, z}
A ∪ B' = {s, t, x, y, z}
Step 3: Find A ∩ B
Common elements in A and B:
A ∩ B = {x}
Step 4: Final Answer
(A ∪ B') ∩ (A ∩ B)
= {s, t, x, y, z} ∩ {x}
= {x}
Final Answer:
{x}