Need this multiple choice assingment Let X andY be two sets

Need this multiple choice assingment:

Let X andY be two sets with n elements in each set. Which of the followings is a FALSE statement? (A) XUY may have 2n elements (B) XnY may have n elements (C) XnY (D) XUY Let X and y be two sets such that X C y and |y| = n. Which of the followings is a TRUE statement? (A) XUY has 2n elements (B) XnY has n elements. (C) XUY has n elements (D) XnY has no elements Let X and Y be two disjoint sets with n ele Which of the followings is a TRUE statement? (A) XUY has 2n elements (B) XnY has n elements. (C) XUY has strictly less than n elements. (D) XUY has strictly less than 2n elements In a survey of college students, 82 use Facebook. 42 use Google+, and 23 use both. Find the number of students in this survey. (A) 144 (B) 124 (C) 147 (D) 101 Y mav have 2n elements mav have no elements mav have no elements ments in each set

Solution

Hi ,

I am answring only first section. Because in second section I am not able to understand what is mean by string in this context (6-digit binary string). So please update same.

1. Here your first question:
   Here X & Y are two sets with n elements:
D. X U Y may have no elements is false.
       Because 1. suppose both sets have different elements then there X U Y have 2n elemnts
               2. suppose both sets have same elements then there X U Y have n elemnts.
  
2.   suppose X = {2,3} & Y = {1,2,3,4,5} and n = 5.
   here X is subset of Y.
   Statement C is true. i.e : X U Y has n elements.
           X U Y = {1,2,3,4,5}
3. Suppose X = {1,2,3,4,5} & Y = {6,7,8,9,10} , n = 5.
   Here X U Y = {1,2,3,4,5, 6,7,8,9,10} i.e 2n = 5*2 = 10
   Ans : A
  
4.    n ( A ) : Set of all students uses facebook = 82
   n ( B ) : Set of all students uses google + = 42
   n ( A B ) = 23
   n ( A B ) = n ( A ) + n ( B ) – n ( A B ) .
               = 82 + 42 - 23
               = 101  
   Ans : D.