Given U={x:x∈N,x≤9}, A={x:x is divisible by 2} and B={x:x3∈N}, where U is the universal set. Then, (A∪B)−(A∩B) = ____.
{2,3,4,8,9}
U={x:x∈N,x≤9}
⇒ U={1, 2, 3, 4, 5, 6, 7, 8, 9}
A={x:x is divisible by 2}
⇒A={2, 4, 6, 8}
B={x:x3∈N}
⇒B={3, 6, 9}
A∪B is the set of elements belonging to A or B.
⇒A∪B={2, 3, 4, 6, 8, 9}
A∩B is the set of elements belonging to both A and B.
⇒A∩B={6}
(A∪B)−(A∩B) is the set of elements belonging to only A∪B, and not (A∩B).
∴(A∪B)−(A∩B)={2, 3, 4, 6, 8, 9}−{6}
={2,3,4,8,9}