If A = {2, 3, 4, 5}, B = {2, 3, 5, 7} and C = {1, 3, 5}, then verify \(A\cup (B\cup C)=(A\cup B)\cup C\).

If A =\(\left\{ -\frac { 1 }{ 2 } ,0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2 \right\} \), B =\(\left\{ 0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2,\frac { 5 }{ 2 } \right\} \) and C =\(\left\{ -\frac { 1 }{ 2 } .\frac { 1 }{ 4 } ,1,2,\frac { 5 }{ 2 } \right\} \), then verify \(A\cap (B\cap C)=(A\cap B)\cap C\) .

If P = {1,2,5,7,9}, Q = {2, 3, 5, 9, 11}, R = {3, 4,5 7, 9} and S = {2, 3, 4, 5, 8}, then find
(i) \((P\cup Q)\cup R\)
(ii) \((P\cap Q)\cap S\)
(iii) \((Q\cap S)\cap R\)

Test for the commutative property of union and intersection of the sets
P = { x : x is a real number between 2 and 7} and
Q = { x : x is an rational number between 2 and 7}.

If A = {p, q, r, s}, B = {m, n, q, s, t} and C = {m, n, p, q, s}, then verify the associative property of union of sets.

Verify the associative property of intersection of sets for A =\(\{ -11,\sqrt { 2 } ,\sqrt { 5 } ,7\} \), B =  \(\\ \{ \sqrt { 3 } ,\sqrt { 5 } ,6,13\} \) and C = \(\{ \sqrt { 2 } ,\sqrt { 3 } ,\sqrt { 5 } ,9\} \).

If A = { x : x = 2ⁿ, n \(\in \) W and n < 4}, B = {x : x = 2n, n \(\in \) N and n ≤ 4} and C = {0, 1, 2, 5, 6} , then verify the associative property of intersection of sets.

If A = {0, 2, 4, 6, 8}, B = {x : x is a prime number and x < 11} and C = {x : x ∈ N and 5 ≤ x < 9} then verify \(A\cup (B\cap C)=(A\cup B)\cap (A\cup C)\).

State Associative property of sets.

State the formula to find \(n\left( A\cup B\cup C \right) \)