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Sets are not determined by algebraic expressions: they are simply collections of elements. The only requirement is that given any element, it is possible to decide whether or not it belongs to the set.
The following, for example, is a set: {yellow, 7.9, April, moon, happy, squirrel}. It is a set of six things (words) I though of while writing this answer. No algebraic expressions will explain the meaning of that set.
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What is an algebraic structure?
An algebraic structure is a set with certain operations defined on the set.The set may consist of numbers but may be collections of matrices, or of permutations and, the operations will depend on the elements of the set.
Why are distributive property commutative property associate property and identity property called properties?
These are characteristics of the elements of algebraic structures, or algebraic sets. Each element in the set possesses these characteristics and that is why they are called properties.
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
Do the intersection of two sets always contains a smaller number of terms than the union of two sets?
No, because the intersection of two equivalent sets will have a union the same size as its intersection.
What is the answer when solving an equation?
In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality). These expressions contain one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled. To be precise, what is sought are often not necessarily actual values, but, more in general, mathematical expressions. A solution of the equation is an assignment of expressions to the unknowns that satisfies the equation; in other words, expressions such that, when they are substituted for the unknowns, the equation becomes an identity
