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Consider the following statements: 1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets. 2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets. Which of the above statements is/are correct?

Consider the following statements: 1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets. 2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets. Which of the above statements is/are correct? Correct Answer Both 1 and 2

Concept:

Equivalent set:  When two sets, for example, A and B have the same cardinality if there exists an objective function from set A to B are called Equivalent set, i.e n(A) = n(B).

Equal set: Two sets for example A and B can be equal only if each element of set A is also the element of the set B. If two sets are the subsets of each other, they are said to be equal. So, it can be written as,

A = B

A ⊂ B and B ⊂ A ⟺ A = B

 

Calculation:

From the definition of equivalent and equal set we can see that;

Statement 1 is true because the number of elements in A = Number of elements in B = 3

Statement 2 is true because {1, 5, 9} ∈ A and {1, 5, 9} ∈ B

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