[a+1/b]^m[a-1/b]^n/[b+1/a]^m[b-1/a]^n=[a/b]^m+n

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\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

Let n(A) = m and n(B) = n. Then the total number of non-empty relations that can be defined from

A to B is
(a) mⁿ
(b) n^m − 1
(c) mn − 1
(d) 2^mn − 1

a, 2 b

2 a, b

a, b \in R .

m^{t h}

a : b

a = x^{m + n} . y^{1}; b = x^{n + 1} . y^{m}

c = x^{1 + m} . y^{n}

a^{m - n} . b^{n - 1} . c^{1 - m} = 1

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