Question

draw Venn diagram which represents A' union B'​

Answer 1

Answer:

$\Huge\fbox{\color{red}{helo.. \: }}$

Union of two sets: ∪

This is a two-circle Venn diagram. The green circle is A, and the blue circle is B. The complete Venn diagram represents the union of A and B, or A ∪ B.

Answer 2

Answer:

hloo bachaa partyyyy.......I know yeee bohot bda h but sahi explained h

Step-by-step explanation:

The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram.

Let A and B be the two sets. The union of A and B is the set of all those elements which belong either to A or to B or both A and B.

Now we will use the notation A U B (which is read as ‘A union B’) to denote the union of set A and set B.

Thus, A U B = {x : x ∈ A or x ∈ B}.

Clearly, x ∈ A U B

⇒ x ∈ A or x ∈ B

Similarly, if x ∉ A U B

⇒ x ∉ A or x ∉ B

Therefore, the shaded portion in the adjoining figure represents A U B.

Union of Sets using Venn Diagram

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Thus, we conclude from the definition of union of sets that A ⊆ A U B, B ⊆ A U B.

From the above Venn diagram the following theorems are obvious:

(i) A ∪ A = A (Idempotent theorem)

(ii) A ⋃ U = U (Theorem of ⋃) U is the universal set.

(iii) If A ⊆ B, then A ⋃ B = B

(iv) A ∪ B = B ∪ A (Commutative theorem)

(v) A ∪ ϕ = A (Theorem of identity element, is the identity of ∪)

(vi) A ⋃ A' = U (Theorem of ⋃) U is the universal set.

Notes:

A ∪ ϕ = ϕ ∪ A = A i.e. union of any set with the empty set is always the set itself.