# Algorithms | Misc | Question 13

A set X can be represented by an array x[n] as follows:

Consider the following algorithm in which x,y and z are Boolean arrays of size n:

`algorithm zzz(x[] , y[], z [])` `{` ` ` `int` `i;` ` ` `for` `(i=O; i<n; ++i)` ` ` `z[i] = (x[i] ^ ~y[i]) V (~x[i] ^ y[i])` `}` |

The set Z computed by the algorithm is:**(A)** (X Intersection Y)**(B)** (X Union Y)**(C)** (X-Y) Intersection (Y-X)**(D)** (X-Y) Union (Y-X)**Answer:** **(D)****Explanation:** The expression x[i] ^ ~y[i]) results the only 1s in x where corresponding entry in y is 0. An array with these set bits represents set X ā Y

The expression ~x[i] ^ y[i]) results the only 1s in y where corresponding entry in x is 0. An array with these set bits represents set Y ā X.

The operator āVā results in Union of the above two sets.

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