Free Printable Novi quiz

1.

Let A and B be sets. A relation $\sim$ from A to B is

a)

Subset of $A\cup B$

b)

Subset of $A\times B$

c)

Function from $A$ to $B$

2.

A relation $\sim$ on a set A is reflexive on A if

a)

For some $x\in A,\ x\sim x$

b)

For all $x\in A,\ x\sim x$

3.

Let $A=\left\{1,2,3,4,5\right\}$ and let $\sim=\left\{\left(1,1\right),\left(1,2\right),\left(2,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right)\right\}.$ Then

a)

$\sim$ is reflexive and symmetric

b)

$\sim$ is equivalence relation

c)

$\sim$ is not transitive

4.

Let $A=\left\{1,2,3\right\}$ and $\sim=\left\{\left(1,1\right)\right\}.$ Then $\sim$ is not equivalence relation since $\sim$ is not

a)

Reflexive

b)

Transitive

c)

Symmetric

5.

Let $A=\left\{1,2,3,4,5\right\}.$ Please select all the partitions of $A:$

a)

$\left\{1,2,3,4,5\right\}$

b)

{{1},{2},{3,4},{5}}

c)

{{1},{2,3,4},{1,5}}

d)

{{2},{4,3},{1,2,5}}

6.

Let us consider Z and the relation $\equiv_3.$ Which of the following equivalence classes are equal:

a)

[11]=[2]

b)

[3]=[303]

c)

[4]=[10]

d)

[4]=[11]

7.

If $\sim$ is an equivalence relation, defined on the set A, then for any a∈A,

a)

[a] is empty set

b)

[a] is non empty set

8.

$17\equiv3\ \left(mod\ 7\right)$

a)

True

b)

False

9.

$19\equiv1\ \left(mod\ 11\right)$

a)

True

b)

False

10.

Let $Z_7$ denotes a complete set of congruence classes module 7. Then $\left(Z_7^{\cdot},\odot\right)$ is a group

a)

True

b)

False

11.

$\left(Z_{14},\oplus\right)$ is a group

a)

True

b)

False

12.

$\left(Z_{14},\odot\right)$ is a group

a)

True

b)

False

13.

$\Phi\left(5\right)=4$

a)

True

b)

False

14.

$\Phi\left(7\right)=5$

a)

True

b)

False

15.

If p is a prime number, then

a)

$\Phi\left(p\right)=p$

b)

$\Phi\left(p\right)=p-2$

c)

$\Phi\left(p\right)=p-1$

16.

If m,n are positive integers, then

a)

$\Phi\left(mn\right)=\Phi\left(m\right)\Phi\left(n\right)$

b)

$\Phi\left(mn\right)=\Phi\left(m\right)+\Phi\left(n\right)$

17.

Mark the right answer

a)

$U_5=\left\{\left[1\right],\left[2\right],\left[3\right],\left[4\right]\right\}$

b)

$U_6=\left\{\left[1\right],\left[4\right],\left[5\right]\right\}$

c)

$U_6=\left\{\left[1\right],\left[5\right]\right\}$

Novi quiz

Total questions: 17

Worksheet time: 10mins

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