Question

please solve this 3 and 4 now please​

Answer 1

3. WHAT IS UNIVERSAL SET ?

ans :- 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.

Answer 2

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 consist of all even numbers such that, A = {2, 4, 6, 8, 10, …} and set B consist of all odd numbers, such that, B = {1, 3, 5, 7, 9, …}. The universal set U consist of all natural numbers, such that, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,….}. Therefore, as we know, all the even and odd numbers are a part of natural numbers. Therefore, Set U has all the elements of Set A and Set B.

EXAMPLES

1)Example: Let us say, there are three sets named as A, B and C. The elements of all sets A, B and C is defined as;

A={1,3,6,8}

B={2,3,4,5}

C={5,8,9}

2)Find the universal set for all the three sets A, B and C.

Answer: By the definition we know, the universal set includes all the elements of the given sets. Therefore, Universal set for sets A, B and C will be,

U={1,2,3,4,5,6,8,9}

Explanation : From the above example, we can see that the elements of sets A, B and C are altogether available in Universal set ‘U’. Also, if you observe, no elements in the universal set are repeated and all the elements are unique.