# Describe the law of Identities.

The Law of identities helps in simplifying complex problems into a simpler ones.

## Answer: Various laws of identities are given below.

Go through the explanation understand it in detail.

**Explanation:**

Let sets A, B, C be subsets of a universal set U. Various identity laws associated with these sets are:

1) Identity Law: A ∪ ∅ = A, A ∩ U = A

2) Complement Law: A ∪ A^{c} = U, A ∩ A^{c} = ∅

3) Commutative Laws: A ∪ B = B ∪ A, A ∩ B = B ∩ A

4) Associative Laws: A ∪ (B ∪ C) = (A ∪ B) ∪ C, A ∩ (B ∩ C) = (A ∩ B) ∩ C

5) Distributive Laws: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C), A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

6) De Morgan's Law: (A ∪ B)^{c }= A^{c} ∩ B^{c}, (A ∩ B)^{c }= A^{c} ∪ B^{c}

7) Absorption Laws: A ∪ (A ∩ B) = A, A ∩ (A ∪ B) = A

8) Complements of U and ∅: U^{c} = ∅, ∅^{c} = U

9) Set Difference Law: A∖B = A ∩ B^{c}

Similar to the identities, we can also make use of the operations on set to work upon similar identities, in the case of sets.

### So, these are the various laws of Identities.

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