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Select the correct answer.

Which is the output of the formula [tex]=\operatorname{XOR}(120 \ \textless \ 102 ; 83 = 83 ; 51 \ \textless \ 24)[/tex]?

A. TRUE
B. FALSE
C. 83
D. 24
E. 120

Answer :

Sure, let's break down the problem step by step:

1. Understanding XOR Function:
The XOR (exclusive OR) function outputs TRUE if an odd number of inputs are TRUE. When counting TRUE values among the inputs:
- If there is 1 TRUE and the others are FALSE, the output is TRUE.
- If there are 3 TRUEs, the output is also TRUE (since 3 is odd).
- If there are 0 TRUE or 2 TRUEs, the output is FALSE (since 0 and 2 are even).

2. Evaluating Each Condition:
- [tex]\( 120 < 102 \)[/tex]: This is FALSE because 120 is greater than 102.
- [tex]\( 83 = 83 \)[/tex]: This is TRUE because 83 is equal to 83.
- [tex]\( 51 < 24 \)[/tex]: This is FALSE because 51 is greater than 24.

3. Applying the XOR Function:
- We have the logical values: FALSE, TRUE, FALSE.
- XORing these values:
- XOR(FALSE, TRUE) is TRUE (since one is TRUE and one is FALSE).
- XOR(TRUE, FALSE) is TRUE (since the result from the previous step is still TRUE and the next value is FALSE).

Therefore, the XOR of FALSE, TRUE, and FALSE results in TRUE.

4. Final Output:
- The final output would thus be TRUE.

So, the correct answer is:

A. TRUE

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