In the group $G = \{1, 2, 3, 4, 5, 6\}$ under $\otimes_{7}$,the solution of $4 \otimes_{7} x = 5$ is

The set $\{-1, 0, 1\}$ is not a multiplicative group because of the failure of

For each binary operation $^*$ defined below,determine whether $^*$ is commutative or associative. On $Z^+$,define $a ^* b = a^b$.

Determine which of the following binary operations on the set $N$ are associative and which are commutative: $a \ast b = 1$ for all $a, b \in N$.

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a ^* b = a - b$. Determine whether the operation $^*$ is commutative and associative.

Which of the following statements is false?