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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?

  • a)
    1 only

  • b)
    2 only

  • c)
    Neither 1 nor 2

  • d)
    Both 1 and 2

  • e)
    Either 1 or 2

Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following statements:1. A = {1, 3, 5} and B = {2, 4, 7} a...
Concept:


Equivalent set: Two sets A and B are said to be equivalent if they have the same number of elements (cardinality), regardless of what the elements are. , i.e n(A) = n(B).


Equal set: Two sets A and B are said to be equal if they have exactly the same elements. The repetition of elements does not matter in sets because a set is defined as a collection of distinct objects, so repeated elements are generally ignored.


If A = B, then n(A) = n(B) and for any x ∈ A, x ∈ B too.


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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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?a)1 onlyb)2 onlyc)Neither 1 nor 2d)Both 1 and 2e)Either 1 or 2Correct answer is option 'D'. Can you explain this answer?
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