Identifying the Incorrect XOR Logic Expression

The question asks to identify the incorrect logical expression involving the XOR (exclusive OR) operator, denoted by $\oplus$. The XOR operation yields a true (1) if the inputs differ and a false (0) if they are the same.

Key properties of XOR used here:

• $A \oplus 0 = A$
• $A \oplus A = 0$
• $A \oplus 1 = \text{NOT } A$
• XOR is associative: $(A \oplus B) \oplus C = A \oplus (B \oplus C)$

Evaluating Each Expression

Option 1: $1 \oplus 0 = 1$

According to the property $A \oplus 0 = A$, substituting $A=1$ gives $1 \oplus 0 = 1$. This expression is correct.

Option 2: $1 \oplus 1 \oplus 1 = 1$

Evaluate step-by-step using associativity:

1. First, calculate $1 \oplus 1$. Since the inputs are the same, the result is 0.
2. Then, calculate $0 \oplus 1$. Since the inputs are different, the result is 1.

So, $(1 \oplus 1) \oplus 1 = 0 \oplus 1 = 1$. This expression is correct.

Option 3: $1 \oplus 1 \oplus 0 = 1$

Evaluate step-by-step:

1. First, calculate $1 \oplus 1$. Since the inputs are the same, the result is 0.
2. Then, calculate $0 \oplus 0$. Since the inputs are the same, the result is 0.

So, $(1 \oplus 1) \oplus 0 = 0 \oplus 0 = 0$. The expression states the result is 1, but the actual result is 0. Therefore, this expression is incorrect.

Option 4: $1 \oplus 1 = 0$

According to the property $A \oplus A = 0$, substituting $A=1$ gives $1 \oplus 1 = 0$. This expression is correct.

Conclusion

The expression $1 \oplus 1 \oplus 0 = 1$ evaluates to 0, making it the incorrect logic expression among the choices.