Exams › JEE Main › Maths

Consider the following statements: Statement-1: If B = U \ A, then n(B) = n(U) − n(A), where U denotes the universal set. Statement-2: For any three sets A, B and C, if C = A − B, then n(C) = n(A) − n(B). Which of the following is correct?

1. Statement-1 is true, and Statement-2 correctly explains Statement-1.
2. Statement-1 is true, but Statement-2 does not correctly explain Statement-1.
3. Statement-1 is false, while Statement-2 is true.
4. Statement-1 is true, while Statement-2 is false.

Correct answer: Statement-1 is true, but Statement-2 does not correctly explain Statement-1.

Solution

Statement-1 is accurate because the number of elements in the complement of set A within the universal set U is indeed the total number of elements in U minus those in A. However, Statement-2 is misleading as it implies a general rule that does not hold when B is not a subset of A, thus it does not correctly explain Statement-1.

Related JEE Main Maths questions

• Let A be the set \(\{(n,2n): n \in \mathbb{N}\}\) and let B be the set \(\{(2n,3n): n \in \mathbb{N}\}\). What is the intersection \(A \cap B\)?
• Let A = \(\{ax : x \in \mathbb{N}\}\) and suppose \(B \cap C = \mathbb{N}\), where b and c are natural numbers that are relatively prime. Then which of the following must be true?
• A class has 55 students. Among them, 23 study Mathematics, 24 study Physics, and 19 study Chemistry. Also, 12 study both Mathematics and Physics, 9 study both Mathematics and Chemistry, 7 study both Physics and Chemistry, and 4 study all three subjects. How many students study exactly one subject?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?

⚔️ Practice JEE Main Maths free + battle 1v1 →