An algebraic structure _________ is called a semigroup.ans.(Q, +, *)(P, +)(P, *)(+, *) Previous Marked for Review Next

A semigroup is defined in abstract algebra as a set equipped with a binary operation that is associative. In this context, you seem to be looking for the correct answer filled in the blank regarding the definition of a semigroup.

Key Definitions:

1. Set (Q, +, *): It represents a set $Q$ and two operations, addition $+$ and multiplication $*$.
2. Set (P, +): It refers to a set $P$ with the addition operation.
3. Set (P, *): It denotes a set $P$ with the multiplication operation.
4. Set (+, *): This seems to indicate the operations without a specified set.

Answer:

Thus, the correct answer to the statement "An algebraic structure _________ is called a semigroup" is:

• *(Q, ) if $*$ is associative.

Therefore, a semigroup is represented as a structure like $(S, *)$ where $S$ is a set and $*$ is an associative binary operation defined on $S$.