Question

if a{a,b,d},B= {b,c,d} then find AUB,BUA, AUB,BUA what do notice​

Answer 1

Step-by-step explanation:

Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Then, A U B is represented as the set containing all the elements that belong to both the sets individually. Mathematically,

A U B = {x : x ϵ A or x ϵ B}

So, A U B = {2, 4, 6, 8, 10, 12},

here the common elements are not repeated.

Properties of (A U B)

Commutative law holds true as (A U B) = (B U A)

Associative law also holds true as (A U B) U {C} = {A} U (B U C)

Let A = {1, 2} B = {3, 4} and C = {5, 6}

A U B = {1, 2, 3, 4} and (A U B) U C = {1, 2, 3, 4, 5, 6}

B U C = {3, 4, 5, 6} and A U (B U C) = {1, 2, 3, 4, 5, 6}

Thus, the law holds true and is verified.

A U φ = A (Law of identity element)

Idempotent Law – A U A = A

Law of the Universal set (U): (A U U