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.