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Let A = {2, 3, 4, 5, ..., 30} and '≈' be an equivalence relation on A × A, defined by (a, b) ≈ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to:
  • a)
    5
  • b)
    6
  • c)
    8
  • d)
    7
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Let A = {2, 3, 4, 5, ..., 30} and ≈ be an equivalence relation o...
A = {2, 3, 4, 5, ..., 30}
(a, b) ≈ (c, d) ⇒ ad = bc
(4, 3) ≈ (c, d) ⇒ 4d = 3c
⇒ 4/3 = c/d
c/d = 4/3 and c, d ∈ {2, 3, ..., 30}
(c, d) = {(4, 3), (8, 6), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)}
No. of ordered pairs = 7
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Community Answer
Let A = {2, 3, 4, 5, ..., 30} and ≈ be an equivalence relation o...
B = {4, 8, 12, 16, ..., 28}.

To find the intersection of sets A and B, we need to find the common elements between the two sets.

Looking at set A, we see that it contains all the even numbers from 2 to 30.

Looking at set B, we see that it contains all the numbers that are multiples of 4 from 4 to 28.

Therefore, the intersection of sets A and B would be the set of numbers that are both even and multiples of 4. These numbers are 4, 8, 12, 16, 20, 24, and 28.

So, the intersection of sets A and B is {4, 8, 12, 16, 20, 24, 28}.
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Let A = {2, 3, 4, 5, ..., 30} and ≈ be an equivalence relation on A × A, defined by (a, b) ≈(c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4, 3) is equal to:a)5b)6c)8d)7Correct answer is option 'D'. Can you explain this answer?
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