If A = {1, 2, 3, 4}, how many subsets of A contain 1 but do not contain 4?
Answer and explanation
Correct answer: 4
The element 1 is compulsory, while 4 is forbidden. Thus, only 2 and 3 remain available for independent selection. Each of these two elements can be either included or excluded, giving 2² = 4 possible subsets. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Hence option B is correct. Fixed inclusion and exclusion conditions should be handled before counting the free elements.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The element 1 is compulsory, while 4 is forbidden. Thus, only 2 and 3 remain available for independent selection. Each of these two elements can be either included or excluded, giving 2² = 4 possible subsets. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Hence option B is correct. Fixed inclusion and exclusion conditions should be handled before counting the free elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
