. a) A and B are two sets such that n(A) = 3 and n(B) = 2. If (a ,3), (6,2) and (0,3) are in A x B, find the sets A and B and also find A x B where a, b, c are distinct elements. b) IfR is a relation given by {(x,y) : x EN,y e N and x + y = 12 } then represent the relation using an arrow diagram. Also write the relation in Roster form and find its domain and range.
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Given, A and B are two sets such that n(A) = 3 and n(B) = 2.
(x, 1), (y, 2) and (z, 1) ∈ A × B.
Since (x, 1), (y, 2) and (z, 1) are elements of A × B.
∴ x, y and z are elements of A and 1, 2 are elements of B.
Now, n(A × B) = n (A) × n(B) = 3 × 2 = 6
So, A = {x, y, z} and B = {1, 2}.
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