From the sets given below, select equal sets: A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2} E = {–1, 1}, F = {0, a}, G = {1, –1}, H = {0, 1}
The equal sets are: B = D and E = G.
Explanation
Two sets are equal if they have exactly the same elements. The order of elements does not matter, and repetition of elements in a set does not change the set. From the given sets, B = {1, 2, 3, 4} and D = {3, 1, 4, 2} contain the same elements {1, 2, 3, 4}, so B = D. Similarly, E = {–1, 1} and G = {1, –1} contain the same elements {–1, 1}, so E = G. All other sets have different elements and are not equal.
Solution Steps
Step 1: List all sets: A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}, E = {–1, 1}, F = {0, a}, G = {1, –1}, H = {0, 1}
Step 2: Compare B = {1, 2, 3, 4} and D = {3, 1, 4, 2}. Both have same elements {1, 2, 3, 4}. B = D
Step 3: Compare E = {–1, 1} and G = {1, –1}. Both have same elements {–1, 1}. E = G
Step 4: All other sets have different elements, so no other equal pairs exist.