Statement 1 : A = {x, y, z, w}, B = {x | x ≤ 4, x ∈ N}. Sets A and B are equivalent sets.
Statement 2 : All equal sets are equivalent sets but all equivalent sets may or may not be equal sets.
Which of the following options is correct ?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1 : A = {x, y, z, w}, so n(A) = 4. B = {x | x ≤ 4, x ∈ N} = {1, 2, 3, 4}, so n(B) = 4. Since n(A) = n(B), the sets are equivalent. Statement 1 is true.
Statement 2 : Equal sets have the same elements, so they are always equivalent. However, equivalent sets only have the same number of elements and may or may not be equal. Statement 2 is true.
Hence, Option 1 is the correct option.