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Let $X=\{1,2,3\}$, $Y=\{1,2,3,4\}$, and $Z=\{1,2\}$

(a) Define a function $g:X\rightarrow Z$ that is onto but not one-one

(b) Define a function $h: Y\rightarrow Y$ that is neither one-to-one nor onto

for (a) suppose we define $g(1)=1,g(2)=2,g(3)=2$ Is right ?

for (b) $h(1)=h(2)=h(3)=h(4)=1$ Is right ?

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  • $\begingroup$ Yes! It's correct. $\endgroup$ – André Porto Nov 9 '16 at 4:41
  • $\begingroup$ @vidyarthi...g is not one one $\endgroup$ – user293581 Nov 9 '16 at 4:43
  • $\begingroup$ @rajendra yes, i mistook onto for one-one. You are right. $\endgroup$ – vidyarthi Nov 9 '16 at 4:45
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Yes, your answers are quite correct.

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