Question

The sample space is given as {1, 2, 3, 4, 5, 6, 7, 8, 9}. a union b ={1,2,3}. find a' insect b'.

a) {4,5,6,7,8,9}
b) {1,2,3}
c) {1,2,3,4,5,6,7,8,9}
d) none of the above

Answer 1

To find A' intersect B', we determine the complement of A union B within the sample space S and then find the common elements between the two complements. The answer is option a) {4,5,6,7,8,9}.

Step-by-step explanation:

To solve this problem, we need to understand the concepts of complementary sets and intersection of sets. The complement of a set A, denoted as A', is the set of all elements in the sample space S that are not in A. Similarly, the complement of set B (B') is the set of all elements in S that are not in B.

The student has provided the union of sets A and B as {1,2,3}. To find the complements A' and B', we consider all elements of the sample space S that are not in the union. Since S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, the complements A' and B' are the same and include all elements that are not in A union B, which are {4, 5, 6, 7, 8, 9}.

Now, to find A' intersect B' (A' ∩ B'), we look for elements that are common to both A' and B'. Since A' and B' are identical in this case, the intersection is also {4, 5, 6, 7, 8, 9}. Hence, the correct answer is option a) {4,5,6,7,8,9}.