Representing Sets in binary string?

In summary, the conversation is discussing how to represent two sets, X and Y, on a new set K using binary strings. A binary string consists of 0s and 1s and indicates whether a number is in the set or not. X and Y can be represented on K by using a binary string to show which numbers are in each set.
  • #1
rclakmal
76
0

Homework Statement





X={4,8,12,16}
Y={2,6,10,12}
K=X U Y(union)

They asked to represent X and Y on K using binary String >i don't know how to do this please help .What is meant by Binary String ?


Homework Equations





The Attempt at a Solution

 
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  • #2
I think they mean a string of numbers which are 0 or 1, and which indicate whether a number is in the set or not.
For example, you could represent S = {1, 2, 3, 6, 7} by
1100111
where the rightmost 1 indicates that 1 is in S, the 1 to the left of that indicates that 2 is in S, the third 1 from the right that 3 is in S, then two zeroes meaning 4 and 5 are not in S, etc.
 
  • #3
ok thanks for the help ,,,,,,but what does it mean by "X and Y on K" .?
 

1. What is binary string representation?

Binary string representation is a way of representing a set using a sequence of 0s and 1s. Each element in the set is mapped to a binary digit, with 0 representing absence and 1 representing presence.

2. Why is binary string representation used for sets?

Binary string representation is used for sets because it is a compact and efficient way of representing large sets. It also allows for easy implementation of set operations, such as union and intersection.

3. How do you convert a set to binary string representation?

To convert a set to binary string representation, you can use the following steps:

  • Assign a binary digit to each element in the set, with 0 representing absence and 1 representing presence.
  • Order the elements in the set in a consistent manner.
  • Write the binary digits in the order of the elements, with each digit separated by a comma.

For example, the set {1, 3, 5, 7} can be represented as 1010101.

4. Can binary string representation handle infinite sets?

No, binary string representation is not suitable for handling infinite sets. It is only applicable for finite sets.

5. How do you perform set operations on binary string representations?

To perform set operations on binary string representations, you can use logical operators (AND, OR, NOT) to compare the binary digits of two sets. For example, to find the union of two sets A and B, you can use the logical OR operator on their binary string representations. The resulting binary string will represent the union of A and B.

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