1. Let X and Y be two sets with n elements in each set. Which of the followings
ID: 3147119 • Letter: 1
Question
1. Let X and Y be two sets with n elements in each set. Which of the followings is a FALSE statement? (A) X may have no elements. (B) XUY may have no elements (C) XUY may have 2n elements. (D) XnY may have n elements. 2. Let X and Y be two sets such that X C Y and = n. Which of the followings is a TRUE statement? (A) XUY has 2n elements. (B) XnY has no elements. (C) XnY has n elements. (D) XUY has n elements. 3. Let X and Y be two disjoint sets with n elements in each set. Which of the followings is a TRUE statement? (A) XnY has n elements. (B) XUY has strictly less than n elements. (C) XUY has 2n elements. (D) XUY has strictly less than 2n elements. 4. In a survey of college students, 1002 use Snapchat, 420 use Whatsapp, and 230 use both. Find the number of students in this survey. (A) 1652 (B) 1562 (C) 1192 (D) 1992 5. How many 6-digit binary strings are there with three 1's? (A) 20 (B) 10 (C) 1 (D) 6Explanation / Answer
1) B) X U Y may have no elements.
As it is given that there are n elements in each set then it is impossible for their union to be a null set.
2) D)X U Y have n elements.
As all the elements of X belong in Y.
3) C)X U Y have 2n elements.
Disjoint sets have no element in common so there will b 2n elements in their union.
For next questions use formula C(n,k) where n is the no. of binary digits and k is the no. of 0's or 1's
4) C) 1192
As (1002+420) -230=1192
5) A) 20
6) B)7
7)C) 56
Adding for both four 1's and two 1's
8) C)12870
9)C) 8008
10) B)20
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