1.
For any set A, (A')' is equal to
Correct Answer
B. A
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.
2.
The symmetric difference of A={1,2,3} and B={3,4,5} is,
Correct Answer
B. {1,2,4,5}
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}.
3.
In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is
Correct Answer
C. 60%
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%.
4.
If A={1,2,3,4,5} then the number of the proper subsets of A is
Correct Answer
C. 31
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.
5.
In school, there are 20 teachers who teaches mathematics or physics. Of these, 12 teaches mathematics and 4 teaches physics and mathematics. How many teaches physics?
Correct Answer
B. 8
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.
6.
How many elements are there in the power set of null set?
Correct Answer
B. 1
7.
If A and B are two sets having 3 and 6 elements respectively. What is the minimum number of elements present in AUB?
Correct Answer
C. 6
Explanation
.
8.
If a set contains n elements, then the number of elements in the power set
Correct Answer
B. 2^{n}
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.
9.
In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea.
How many drink tea and coffee both?
How many drink coffee but not tea?
Correct Answer
B. 16,20
Explanation
Total number of people: 50
People who drink tea but not coffee: 14
People who drink tea: 30
Step 1: Calculate the number of people who drink both tea and coffee
People who drink tea: 30 People who drink tea but not coffee: 14
Number of people who drink both tea and coffee: 30−14=16
Step 2: Calculate the number of people who drink coffee but not tea
First, find the total number of people who drink coffee:
Total people: 50 People who drink tea: 30 Number of people who drink neither or only coffee: 50−30=20
Since we already know 16 people drink both tea and coffee, the number of people who drink only coffee is: 20−16=4
Summary
The number of people who drink both tea and coffee is 16.
The number of people who drink coffee but not tea is 4.
10.
A set can have infinitely many subset true or false?
Correct Answer
A. True
Explanation
A set can indeed have infinitely many subsets if the set itself is infinite. For example, the set of natural numbers {1, 2, 3, ...} is infinite, and it has infinitely many subsets. This includes subsets like {1}, {1, 2}, {2, 3}, and so on, as well as the empty set and the set itself. Hence, the statement is true for infinite sets.