SET THEORY (CDS)Total Questions: 1411. Out of 105 students taking an examination English and Mathematics, 80 students pass in English, 75 students pass in Mathematics 10 students fail in both the subjects. How many students pass in only one subject? [2015 (I) Morning Shift ](a) 26(b) 30(c) 35(d) 45Correct Answer: (d) 45Solution:Number of students failing in Mathematics = 105 -75 = 30 Number of students failing in English = 105 - 80 = 25 ∴ Number of students failing in 1 subject = (25 + 30) - 10 = 4512. If A and B are any two non-empty subsets of a set E, then what is A ∪ (A ∩ B) equal to? [2015 (I) Morning Shift ](a) A ∩ B(b) A ∪ B(c) A(d) BCorrect Answer: (c) ASolution:Since, A and B are non-empty subsets of E.13. If A is a non-empty subset of a set E, then what is E ∪ (A ∩ φ) - (A - φ) equal to? [2015 (I) Morning Shift ](a) A(b) Complement of A(c) φ(d) ECorrect Answer: (d) ESolution:14. Let A and B be finite non-empty sets with the number of elements in A = m and number of elements in B = n. Let m > n If for some integer k ≥ 1 the number of non-empty subsets of A= 2ᵏ + the number of non-empty subsets of B₁ then which one of the following is correct? [2015 (I) Morning Shift ](a) m = n + 2(b) m = n + 1(c) m = n + p for some odd prime number p(d) m = n + t for some composite number tCorrect Answer: (b) m = n + 1Solution:According to the question,Submit Quiz« Previous12