If A is the set of 4-digit multiples of 2, B is the set of 4-digit multiples of 5, and U is the set of all 4-digit numbers, express using union, intersection, and complement notation:
a: Set C of 4-digit multiples of both 2 and 5
A) C=U\(A∪B)
B) C=(A∪B)∩U
C) C=(A∩B)∩U
D) C=A∪(B∩U)
b. Set D of 4-digit multiples of at least one of 2 or 5
A) D=U\(A∪B)
B) D=(A∪B)∩U
C) D=(A∩B)∩U
D) D=U\(A∩B)
c. Set E of 4-digit numbers that are neither multiples of 2 nor multiples of 5?
A) E=U\(A∪B)
B) E=U\(A∩B)
C) E=U∩(A\B)
D) E=A∩B∩U
a: C
b: B
c: A
Sebi is correct!
a: Set C of 4-digit multiples of both 2 and 5
The correct answer is D) C=A∪(B∩U)
b. Set D of 4-digit multiples of at least one of 2 or 5
The correct answer is A) D=U\(A∪B)
c. Set E of 4-digit numbers that are neither multiples of 2 nor multiples of 5
The correct answer is B) E=U\(A∩B)
a: Set C of 4-digit multiples of both 2 and 5
To find the set of 4-digit multiples of both 2 and 5, we need to find the intersection of sets A and B.
The intersection of two sets, denoted by ∩, represents the elements that are common to both sets.
In this case, A represents the set of 4-digit multiples of 2, and B represents the set of 4-digit multiples of 5. So, the intersection of A and B would be the set of 4-digit numbers that are divisible by both 2 and 5.
The correct notation for set C would be C = A ∩ B.
Therefore, the correct option is:
C) C = (A ∩ B) ∩ U
b. Set D of 4-digit multiples of at least one of 2 or 5
To find the set of 4-digit multiples of at least one of 2 or 5, we need to find the union of sets A and B.
The union of two sets, denoted by ∪, represents all the elements that are in either one or both sets.
In this case, A represents the set of 4-digit multiples of 2, and B represents the set of 4-digit multiples of 5. So, the union of A and B would be the set of 4-digit numbers that are divisible by either 2 or 5, or both.
The correct notation for set D would be D = A ∪ B.
Therefore, the correct option is:
B) D = (A ∪ B) ∩ U
c. Set E of 4-digit numbers that are neither multiples of 2 nor multiples of 5
To find the set of 4-digit numbers that are neither multiples of 2 nor multiples of 5, we need to find the complement of the union of sets A and B.
The complement of a set, denoted by ', represents all the elements that are not in that set.
In this case, A represents the set of 4-digit multiples of 2, and B represents the set of 4-digit multiples of 5. The union of A and B would be the set of 4-digit numbers that are divisible by either 2 or 5, or both. To find the numbers that are neither multiples of 2 nor multiples of 5, we need to find the complement of this union.
The correct notation for set E would be E = U \ (A ∪ B).
Therefore, the correct option is:
B) E = U \ (A ∪ B)