Question

$a \oplus b = 1$ if $a,b>0$ or $a,b<0$; \quad $a \oplus b = -1$ otherwise.
What is $(2 \oplus 0) \oplus (-5 \oplus -6)$?
Statement A
A. $a \oplus b = 0$ if $a=0$
Statement B
B. $a \oplus b = b \oplus a$

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

Sometimes one property (like value when one argument is zero) is enough to evaluate a composite expression.

Answer 1

The Correct Option is A

From Statement A: $2 \oplus 0 = 0$ (since $a=0$ gives result $0$). From definition: $-5 \oplus -6 = 1$ (both negative). Now $(2 \oplus 0) \oplus (-5 \oplus -6) = 0 \oplus 1$ → different signs $\Rightarrow -1$. Statement A alone is enough; Statement B is just commutativity.