Answer: The correct option is (C) A = {1, 2, 3, 4, 5, 7, 8}.
Step-by-step explanation: Given that eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag.
The sample space, S will be
S = {1, 2, 3, 4, 5, 6, 7, 8}.
Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.
Let, 'B' represents the event in which the number 6 is drawn from the bag.
So, B = {6}.
Since 'A' is the complement of 'B', so the set 'A' will contain those element of the sample space 'S' that are not in the set 'B'.
Therefore,
A = B' = {1, 2, 3, 4, 5, 7, 8}
⇒ A = {1, 2, 3, 4, 5, 7, 8}.
Thus, (C) is the correct option.
The subset relation defines a partial order on sets.
The subset A is equal to A = {1, 2, 3, 4, 5, 7, 8}.
Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag.
Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.
The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation.
A = Numbers inside the Bag = {Eight Identical slips of paper numbering from 1 to 8} = {1,2,3,4,5,6,7,8}.
Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.
Let B = Subset of A = Complement of the event in which number 6 is drawn from 8 numbers
Subset A = {1,2,3,4,5,6,7,8} - {6}
Subset A = {1, 2, 3, 4, 5, 7, 8}
Hence, the subset A is equal to A = {1, 2, 3, 4, 5, 7, 8}.
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