Quiz For Class 11

Explanation
The correct answer is A. The given expression (A')' represents the complement of the complement of set A. The complement of A' is the set of all elements that are not in A'. Therefore, the complement of A' is the set of all elements that are in A. Hence, (A')' is equal to set A.

Explanation
The symmetric difference of two sets A and B is the set of elements that are in either A or B, but not in both. In this case, the elements 1 and 2 are in set A but not in set B, and the elements 4 and 5 are in set B but not in set A. Therefore, the symmetric difference of A and B is {1,2,4,5}.

Explanation
The correct answer is 60%. This can be calculated by adding the percentage of people traveling by car (20%) and the percentage of people traveling by bus (50%), and then subtracting the percentage of people traveling by both car and bus (10%). Therefore, 20% + 50% - 10% equals 60%.

Explanation
The number of proper subsets of a set with n elements is given by 2^n - 1. In this case, A has 5 elements, so the number of proper subsets is 2^5 - 1 = 32 - 1 = 31.

Explanation
Based on the information given, there are a total of 20 teachers who teach either mathematics or physics. Out of these, 12 teachers teach mathematics and 4 teachers teach both physics and mathematics. Therefore, the remaining teachers who teach only physics can be calculated by subtracting the number of teachers who teach mathematics from the total number of teachers. So, the correct answer is 20 - 12 = 8.

Explanation
The power set of a set is the set of all possible subsets of that set. The power set of the null set, also known as the empty set, is a set that contains only one element, which is the null set itself. This is because the null set does not contain any elements, so the only possible subset is the null set. Therefore, the power set of the null set has only one element.

Explanation
The minimum number of elements present in AUB is 2. This is because the union of two sets includes all the elements from both sets without any repetition. In this case, set A has 3 elements and set B has 6 elements, but there might be some overlap between the two sets. However, since the question does not provide any information about the elements in the sets or their relationship, we cannot determine the exact number of elements in the union. Therefore, the minimum number of elements in AUB is 2, as there must be at least one common element between the two sets.

Explanation
The power set of a set with n elements is the set of all possible subsets of that set, including the empty set and the set itself. To determine the number of elements in the power set, we can use the concept of binary representation. Each element in the original set can either be included or excluded in a subset, which can be represented by a binary digit (0 for excluded, 1 for included). Since there are n elements, there are 2^n possible combinations of including or excluding each element. However, we also need to consider the empty set, which is always a subset. Therefore, the total number of elements in the power set is 2^n + 1.

Explanation
In the given group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Therefore, the number of people who drink tea is 30. To find the number of people who drink both tea and coffee, we subtract the number of people who drink tea only from the total number of people who drink tea, which is 30 - 14 = 16. Thus, 20 people drink tea and coffee both. Similarly, to find the number of people who drink coffee but not tea, we subtract the number of people who drink tea only from the total number of people who drink coffee, which is 14. Therefore, 16 people drink coffee but not tea.

Explanation
A set can have infinitely many subsets. This is because every element in a set can either be included or excluded from a subset, resulting in a total of 2^n possible subsets, where n is the number of elements in the set. Therefore, the statement "A set can have infinitely many subsets" is true.