Question

Given the following sets, find the set A′∩(B ∩ C′).

U= {1,2,3,7}
A={1,2,3,5}
B={1,2,3}
C={1,2,3,4,5}
a) {4,5,7}
b) {4,5}
c) {1,2,3}
d) {1,2,3,4,5,7}

Answer 1

It represents the intersection of the complement of A and the intersection of B and the complement of C. Therefore, the correct answer is option c) {1,2,3}

Step-by-step explanation:

The set A′∩(B ∩ C′) is the intersection of the complement of set A (denoted as A′) and the intersection of sets B and the complement of C (denoted as B ∩ C′). Let's break down the solution step by step:

The complement of set A includes all elements in the universal set U that are not in A. In this case, A′ = {4, 5, 6, 7, 8, 9, 0}.

The intersection of sets B and C′ includes elements that are common to B and not in C. In this case, B ∩ C′ = {4}.

The final intersection is the common elements between A′ and (B ∩ C′). Therefore, the answer is {1, 2, 3}, as these are the elements present in both A′ and (B ∩ C′).

In summary, the final answer is c) {1, 2, 3}, as these are the elements in the intersection of the complement of A and the intersection of B and the complement of C.