Let f:$${x$$,y,$$z}$$→$${1$$,$$2$$,$$3}$$ be a $$one-one$$ mapping such that only one of the following three statements is true and remaining two are false: $$f(x)$$≠$$2$$,$$f(y)=2$$,$$f(z)$$≠$$1$$, then

Question

Let f:$${x$$,y,$$z}$$→$${1$$,$$2$$,$$3}$$ be a $$one-one$$ mapping such  that only one of the following three statements is true and  remaining two are false: $$f(x)$$≠$$2$$,$$f(y)=2$$,$$f(z)$$≠$$1$$, then

Infinity Learn · Accepted Answer

case $$1$$ :  Let fx ≠$$2$$ be true and $$fy=2$$,fz≠$$1$$ are false then fx≠$$2$$,fy≠$$2$$,$$fz=1$$ ⇒ $$fx=3$$ ,$$fy=3$$ ,$$fz=1$$ , which is not $$one-one$$   case $$2$$ :  let fy $$=2$$ be true and fx≠$$2$$,fz≠$$1$$ be false   then    $$fy=2$$ , fx $$=2$$ ,$$fz=1$$ , which is not $$one-one$$    case $$3$$ : let fz≠$$1$$ be true and fx≠$$2$$ ,$$fy=2$$ are false     then   fx $$=2$$ ,fy ≠$$2$$, fz ≠$$1$$ are true      $$f(x)=2$$,$$f(y)=1$$,$$f(z)=3$$, one to one

$Let f : {x, y, z} \to {1, 2, 3} be a one-one mapping such that only one of the following three statements is true and$
$remaining two are false: f (x) \neq 2, f (y) = 2, f (z) \neq 1, then$

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Let f:{x,y,z}→{1,2,3} be a one-one mapping such that only one of the following three statements is true and remaining two are false: f(x)≠2,f(y)=2,f(z)≠1, then

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$Let f : {x, y, z} \to {1, 2, 3} be a one-one mapping such that only one of the following three statements is true and$
$remaining two are false: f (x) \neq 2, f (y) = 2, f (z) \neq 1, then$