19. The operation * on the set $$ R $$ of real numbers is defined by $$ a * b=\frac{2 a-1}{2}+b \text { for all } a, b \in R $$ (a) Is the set $$ R $$ closed under $$ * $$ ? (b) Is the operation*commutative in (c) Is the operation* associative in $$ R $$ ? (d) Determine the identity element in

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(a) Yes, $$ \mathbb{R} $$ is closed under $$ * $$. (b) No, the operation $$ * $$ is not commutative. (c) Yes, the operation $$ * $$ is associative. (d) The identity element is $$ \frac{1}{2} $$.

19. The operation * on the set \( R \) of real numbers is defined by \[ a * b=\frac{2 a-1}{2}+b \text { for all } a, b \in R \] (a) Is the set \( R \) closed under \( * \) ? (b) Is the operationcommutative in (c) Is the operation associative in \( R \) ? (d) Determine the identity element in

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19. The operation * on the set \( R \) of real numbers is defined by \[ a * b=\frac{2 a-1}{2}+b \text { for all } a, b \in R \] (a) Is the set \( R \) closed under \( * \) ? (b) Is the operation*commutative in (c) Is the operation* associative in \( R \) ? (d) Determine the identity element in

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19. The operation * on the set \( R \) of real numbers is defined by \[ a * b=\frac{2 a-1}{2}+b \text { for all } a, b \in R \] (a) Is the set \( R \) closed under \( * \) ? (b) Is the operationcommutative in (c) Is the operation associative in \( R \) ? (d) Determine the identity element in