If U = (1, 2, 3, 6, 7, 8, 9, 10) is the universal set. E = (10, 4, 6, 8, 10) and F = {x: 1x\(^2\) = 2\(^6\), x is odd}. Find (E ∩ F)', where ' means the complement of a set.
A
(0)
B
U
C
(8)
D
\(\phi\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
U = (1, 2, 3, 6, 7, 8, 9, 10)
E = (10, 4, 6, 8, 10)
F = (x : x\(^2\) = 2\(^6\), x is odd)
∴ F = \(\phi\) Since x\(^2\) = 2\(^6\) = 64
x = \(\pm 8\) which is even
∴ E ∩ F = \(\phi\) Since there are no common elements
Since E ∩ F = \(\phi\), then ( E ∩ F)' = U = (1, 2, 3, 6, 7, 8, 9, 10)
Source: Myschool Past Questions Archive (Record #31306)