Hi, help would be greatly appreciated. 1. Let X and Y e two sets with n elements

Question

Hi, help would be greatly appreciated.

1. Let X and Y e two sets with n elements in each set. Which of the followings is a FALSE statement? (A) XUY may have 2n elements. (B) X n Y may have n elements. (C) X nY may have no elements. (D) XUY may have no elements. 2. Let X and Y be two sets such that XCY and IYI n. Which of the followings is a TRUE statement? (A) X UY has 2n elements. (B) XnY has n elements. (C) X U Y has n elements. (D) Xn Y has no 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) X UY has 2n elements. (B) X m Y has n elements. (C) X UY has strictly less than n elements. (D) X U Y has strictly less than 2n elements. 4. In survey college students, use Facebook, 42 use Google-t-, and 23 use both. Find the number of students in this survey. (A) 144 (B) 124 (C) 147 (D) 101 5. How many 6-digit binary strings are there with three 1's? (A) 20 (B) 10 (C) 1 (D) 6 6. How many 6-digit binary strings are there with five 1's?

Explanation / Answer

(Chegg policy allows only four questions to be answered. Please post remaining in a separate question)

1. For disjoint X and Y, the total number of elements in XUY is 2n and for X=Y it is n.

For disjoint X and Y, the total number of elements in XnY is 0 and for X=Y it is n.

So the answer is (D) XUY may have no elements.

2. If X is a subset of Y, total number of elements in X < n. Further XUY = Y and XnY = X. So XUY has n elements and XnY has elss than n elements. The only answer that matches is (C) XUY has n elements.

3. From answer 1 we know that XUY has 2n elements and XnY has 0 elements. So the answer is (A) XUY has 2n elements.

4. Number of facebook users = 82

Number of google+ users = 42

Number of users of both = 23

=> Number of facebook-only users = 82 - 23 = 59

Number of G+only users = 42 -23 = 19

Total number of users = 59 + 19 + 23 = 101 which is (D)

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