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Let A={ 2,3,4,5,....,17,18 } . Let be the equivalence relatio

Question

Let $A = {2, 3, 4, 5, ...., 17, 18}$ . Let $≃$ be the equivalence relation on $A \times A$ , cartesian product of $A$ with itself, defined by $(a, b) ≃ (c, d)$ , iff $a d = b c$ . The the number of ordered pairs of the equivalence class of $(3, 2)$ is

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Olivia Discussed

Let

A = {2, 3, 4, 5, ...., 17, 18}

. Let

≃

be the equivalence relation on

A \times A

, cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

, iff

a d = b c

. The the number of ordered pairs of the equivalence class of

(3, 2)

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Text solutionVerified

Let

(3, 2) ≅ (x, y)

\Rightarrow 3 y = 2 x

This is possible in the cases:

x = 3, y = 2

x = 6, y = 4

x = 9, y = 6

x = 12, y = 3

x = 15, y = 10

x = 18, y = 12

Hence total pairs are

6

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Question Text	Let $A = {2, 3, 4, 5, ...., 17, 18}$ . Let $≃$ be the equivalence relation on $A \times A$ , cartesian product of $A$ with itself, defined by $(a, b) ≃ (c, d)$ , iff $a d = b c$ . The the number of ordered pairs of the equivalence class of $(3, 2)$ is
Answer Type	Text solution:1
Upvotes	150