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Recent questions tagged goclasses_wq12

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 5
Consider the group $0,1,2,3,4,+{ }_{5}$. What will be the value of $2^{-3}$ and $3^{-2}$ for the given group? $1$ and $1$ $2$ and $3$ $4$ and $4$ $3$ and $2$

GO Classes asked in Set Theory & Algebra May 29, 2022

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3 votes

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 6
Let $f$ be a function from a set $X$ to a set $Y$. Consider the following statements. $P:$ For each $x \in X$, there exists $y \in Y$ such that $f(x)=y$. $Q$ : For each $y \in Y$, there exists $x \in X$ ... to-one and onto $Y$ " is $P$ or not $R$ $R$ or not $P$ $R$ or not $Q$ $P$ and not $R$

GO Classes asked in Set Theory & Algebra May 29, 2022

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4 votes

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 9
The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ with addition $\bmod n$ as the operation. How many subgroups of $Z_{9}$ are there?

GO Classes asked in Set Theory & Algebra May 29, 2022

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4 votes

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 10
Let $Z$ be the set of all integers. Let $n \in Z$ and $nZ = \{nk : k \in Z \}.$ We know that $Z$ is a group under addition operation. Which of the following is/are true? $nZ$ is a subgroup of $Z$ (under ... for some $n.$ $3Z$ is the smallest subgroup of $(Z,+)$ containing $3.$ $nZ$ is a cyclic subgroup of $Z.$

GO Classes asked in Set Theory & Algebra May 29, 2022

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4 votes

1 answer

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 11
The set $Z_{\mathrm{n}}^{*}$ consists of the elements $\{1,2, \ldots, \mathrm{n}-1\}$ with multiplication $\bmod n$ as the operation. The group $Z_{n}$ consists of the elements $\{0,1,2, \ldots, n-1\}$ ... then $\mathrm{G}$ is a cyclic group. The number of elements in $Z_{8}^{*}$ which have an inverse is $4.$

GO Classes asked in Set Theory & Algebra May 29, 2022

280 views

2 votes

1 answer

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 12
Consider the standard groups $Z_{\mathrm{n}}, \mathrm{R}^{*}, \mathrm{C}^{*}$ under their standard group operation. Here, $\mathrm{R}^{*}, \mathrm{C}^{*}$ are set of non-zero real numbers, set of non-zero complex numbers, ... $\sqrt{3} \in \mathrm{R}^{*}$ $-\mathrm{i} \in \mathrm{C}^{*}$

GO Classes asked in Set Theory & Algebra May 29, 2022

312 views

5 votes

1 answer

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GO Classes Weekly Quiz 12 | Discrete Mathematics | Group Theory, Functions | Question: 14
Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be maps. Which of the following is/are true? If $f$ and $g$ are both one-to-one functions, then $gof$ is one-to-one. ... $g \circ f$ is one-to-one and $f$ is onto, then $g$ is one-to-one.

GO Classes asked in Set Theory & Algebra May 29, 2022

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