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Answer :
Sure, let's break down the problem step-by-step.
We need to use the `XOR` function in a formula to evaluate the given conditions and determine the output.
First, let's review the conditions provided in the formula:
1. [tex]\(120 < 102\)[/tex]
2. [tex]\(83 = 83\)[/tex]
3. [tex]\(51 < 24\)[/tex]
Let's evaluate each condition:
- [tex]\(120 < 102\)[/tex] is False because 120 is not less than 102.
- [tex]\(83 = 83\)[/tex] is True because 83 is equal to 83.
- [tex]\(51 < 24\)[/tex] is False because 51 is not less than 24.
Now, we will perform an XOR operation on the results.
### Understanding XOR Operation
The XOR (exclusive OR) operation returns true if an odd number of the inputs it processes are true. In simpler terms, it will return true if there is exactly one true condition or three true conditions.
Let's apply the XOR operation step-by-step:
1. Start with the first two conditions:
- False (from [tex]\(120 < 102\)[/tex])
- True (from [tex]\(83 = 83\)[/tex])
The XOR of False and True is True (because one of them is true).
2. Take the result from step 1 and XOR it with the third condition:
- True (result from step 1)
- False (from [tex]\(51 < 24\)[/tex])
The XOR of True and False is True (because one of them is true).
So, performing the XOR operation on all three conditions results in True.
Therefore, the output of the formula [tex]\(=\operatorname{XOR}(120 < 102; 83 = 83; 51 < 24)\)[/tex] is:
A. TRUE
We need to use the `XOR` function in a formula to evaluate the given conditions and determine the output.
First, let's review the conditions provided in the formula:
1. [tex]\(120 < 102\)[/tex]
2. [tex]\(83 = 83\)[/tex]
3. [tex]\(51 < 24\)[/tex]
Let's evaluate each condition:
- [tex]\(120 < 102\)[/tex] is False because 120 is not less than 102.
- [tex]\(83 = 83\)[/tex] is True because 83 is equal to 83.
- [tex]\(51 < 24\)[/tex] is False because 51 is not less than 24.
Now, we will perform an XOR operation on the results.
### Understanding XOR Operation
The XOR (exclusive OR) operation returns true if an odd number of the inputs it processes are true. In simpler terms, it will return true if there is exactly one true condition or three true conditions.
Let's apply the XOR operation step-by-step:
1. Start with the first two conditions:
- False (from [tex]\(120 < 102\)[/tex])
- True (from [tex]\(83 = 83\)[/tex])
The XOR of False and True is True (because one of them is true).
2. Take the result from step 1 and XOR it with the third condition:
- True (result from step 1)
- False (from [tex]\(51 < 24\)[/tex])
The XOR of True and False is True (because one of them is true).
So, performing the XOR operation on all three conditions results in True.
Therefore, the output of the formula [tex]\(=\operatorname{XOR}(120 < 102; 83 = 83; 51 < 24)\)[/tex] is:
A. TRUE
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