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GO Classes Test Series 2024 | Discrete Mathematics | Test 3 | Question: 12

in Set Theory & Algebra retagged by
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4 votes
4 votes

Let $\text{G}$ be a group. Let $g,h,x,y \in \text{G}$ be given. It is given that $x \ast g = h, y \ast g = h$

  1. $x = y$
  2. $x \ast x \ast x = y \ast y \ast y$
  3. $x \ast y \ast x = y \ast x \ast y$

 

  1. Only I
  2. Only II
  3. Only I and III
  4. All of I, II and III
in Set Theory & Algebra retagged by
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1 Answer

3 votes
3 votes
Since, $x\ast g = y\ast g,$ So, by the right cancellation property of a group, we have $x= y.$

So, All three statements are correct.
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