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Argument of a Complex Number

Let A=2,3,4,5...

Question

Let A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of A with itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is
(a) 4
(b) 5
(c) 6
(d) 7

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Solution

(c) 6

The ordered pairs of the equivalence class of (3, 2) are {(3, 2), (6, 4), (9, 6), (12, 8), (15, 10), (18, 12)}.
We observe that these are 6 pairs.

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Similar questions

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

≃

be the equivalence relation on

A \times A,

cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

a d = b c .

Then the number of ordered pairs of the equivalence class of

(3, 2)

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

≃

be the equivalence relation on

A \times A

, cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

a d = b c

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

(3, 2)

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

≃

be the equivalence relation on

A \times A,

cartesian product of

A

with itself, defined by

(a, b) ≃ (c, d)

a d = b c .

Then the number of ordered pairs of the equivalence class of

(3, 2)

A = {2, 3, 4, 5, \dots, 30}

^{'} ≅^{'}

be an equivalence relation on

A \times A,

(a, b) ≅ (c, d),

a d = b c .

Then the number of ordered pairs which satisfy this equivalence relation with ordered pair

(4, 3)

Q. Let A = {1, 2, 3, 4}. Let R be the equivalence relation on

A \times A

defined by (a, b) R (c, d) if a + d = b + c. Find the equivalence class [(1, 3)].

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