Union more

A universal set is a set which contains all the elements or objects of other sets, including its own elements. It is usually denoted by the symbol ‘U’. Suppose Set A consists of all even numbers such that, A = {2, 4, 6, 8, 10, …} and set B consists of all odd numbers, such that, B = {1, 3, 5, 7, 9, …}.

These sets do not overlap. Thus A and B are each a subset of this larger set, called the Universal Set. Definition: A Universal Set is the set of all elements under consideration, denoted by capital. . All other sets are subsets of the universal set.

If all the elements of set A are also elements of set B, then A is a subset of B. This means that subsets can be created from any defined universal set. We should first acknowledge that any universal set is a subset of itself. However, a subset usually has less elements than the universal set from which it is created.

Step 1: Draw a rectangle and label it U to represent the universal set. Step 2: Draw circles within the rectangle to represent the other sets. Label the circles and write the relevant elements in each circle. Step 3: Write the remaining elements outside the circles but within the rectangle.

In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal set leads to Russell’s paradox and is consequently not allowed. However, some non-standard variants of set theory include a universal set.

For the first part, a set of triangles will contain both right angle triangles and isosceles triangles. So, set of triangles will be the universal set.

(ii) For the set of isosceles triangles, the universal set can be the set of triangles or the set of polygons or the set of two-dimensional figures.

five axioms