Let A -1-2-3-4- Let R be the equivalence relation on A - A defined by a - b R c - d if a - d - b - c- Find the equivalence class -1-3-

Let (1, 3) R (x, y) for all (x, y) ϵ A × A. That implies, 1 + y = 3 + x ie., y x = 2. So (x, y) may be (1, 3), (2, 4). Hence [(1,3)] = {(1,3), (2, 4)}. ...

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Standard XII

Mathematics

Definition of Function

Let A =1,2,3,...

Question

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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Solution

Let (1, 3) R (x, y) for all $(x, y) ϵ A \times A$ .

That implies, 1 + y = 3 + x ie., y - x = 2.

So (x, y) may be (1, 3), (2, 4).
Hence $[(1, 3)] = {(1, 3), (2, 4)} .$

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Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A×A defined by (a, b) R (c, d) if a + d = b + c. Find the equivalence class [(1, 3)].

Let (1, 3) R (x, y) for all (x,y)ϵA×A. That implies, 1 + y = 3 + x ie., y - x = 2. So (x, y) may be (1, 3), (2, 4). Hence [(1,3)]={(1,3),(2,4)}.

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)].

Let (1, 3) R (x, y) for all $(x, y) ϵ A \times A$ .

That implies, 1 + y = 3 + x ie., y - x = 2.

So (x, y) may be (1, 3), (2, 4).
Hence $[(1, 3)] = {(1, 3), (2, 4)} .$