xor of the subsets set 11 12 13 14 ans
Answers
Answer:
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Step-by-step explanation:
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Answer:
The XOR of the subsets of the set {11, 12, 13, 14} are
- 11
- 12
- 13
- 14
- 7
- 6
- 5
- 1
- 2
- 3
- 10
- 9
- 8
- 15
- 4
Step-by-step explanation:
XOR Logic:
- Exclusive OR is a logic gate that has two inputs and a single output.
- XOR is a logic device that gives a true or high output when one of the inputs is high and the other input is low,
- When both the inputs are logic high, the output is logic low or false.
- Similarly, when both the inputs are logic low, the output is logic high or true.
Step 1:
To find the XOR of the subsets of the given set, we first find all the subsets of the set {11, 12, 13, 14}.
Subsets = [ {11}, {12}, {13}, {14}, {11,12}, {11,13}, {11,14}, {12,13}, {12,14}, {13,14}, {11,12,13}, {11,12,14}, {11,13,14}, {12,13,14}, {11,12,13,14} ]
Step 2:
XOR of the subsets having only one element is the element itself. Therefore,
- Subset of {11} = 11
- Subset of {12} = 12
- Subset of {13} = 13
- Subset of {14} = 14
Step 3:
XOR of the subsets having two elements is given by logically XORing one element with the other.
- Subset of {11,12} = 11 ^ 12 = 7
- Subset of {11,13} = 11 ^ 13 = 6
- Subset of {11,14} = 11 ^ 14 = 5
- Subset of {12,13} = 12 ^ 13 = 1
- Subset of {12,14} = 12 ^ 14 = 2
- Subset of {13,14} = 13 ^ 14 = 3
Step 4:
XOR of the subsets having three or more elements is given by logically XORing all the elements of the subset.
- Subset of {11,12,13} = (11 ^ 12) ^ 13 = 7 ^ 13 = 10
- Subset of {11,12,14} = (11 ^ 12) ^ 14 = 7 ^ 14 = 9
- Subset of {11,13,14} = (11 ^ 13) ^ 14 = 6 ^ 14 = 8
- Subset of {12,13,14} = (12 ^ 13) ^ 14 = 1 ^ 14 = 15
- Subset of {11,12,13,14} = (11 ^ 12 ^ 13) ^ 14 = 10 ^ 14 = 4
Thus, the XOR of the subsets of the set {11, 12, 13, 14} are 11, 12, 13, 14, 7, 6, 5, 1, 2, 3, 10, 9, 8, 15, 4
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