Question

यदि A = {a, b, c}, B = {u, v, w} यदि f: A→B तथा g: B→A निम्न प्रकार परिभाषित हों कि

f= {(a, v), (b, u), (c, w)}

g= {(u, b), (v, a), (w, c)} तो (fog) तथा (gof) ज्ञात कीजिए।

Answer 1

दिया है, f = {(a, v), (b, u), (c, w)}

g = {(u, b), (v, a), (w, c}}

∴ f(a) = v तथा g(u) = b

f(b) = u तथा g(v) = a

f(c) = w तथा g(w) = c

अत: fog(x) = f[g(x)] से

fog(u) = f[g(u)] = f(b) =u

fog(v) = f[g(v)] = f(a) = v

fog(w) = f[g(w)] =f(c) = w

अत: fog= {(u, u), (v, v), (w, w)}

gof(a) = g[f(a)] = g(v) = a

gof(b) = g[f(b)] = g(u) = b

gof(c) = g[f(c)] = g(w) = c

∴ gof = {(a, a), (b, b), (c, c)}.