CSC M1 #1

A={x∈ℤ:x is odd}B={2,4,6,7,11,12}C={1,3,4,6,11,13}

Select the set corresponding to C⊕(A∩B)

{1,3,4,6,7,13}

Select the set that is equivalent to (B∩C)∪∅

 

B∩C

Select the false

statement.

ℤ⊂ℝ+

Select the collection of sets that forms a partition of ℝ

 

{x∈ℝ:x<2}{x∈ℝ:2≤x<4}{x∈ℝ:4≤x}

The domain of a relation is the set of all positive integers. x is related to y if ⌊x2⌋≤⌊y2⌋. Select the description that correctly characterizes the relation.

 

Neither a partial order nor a strict order

Graph G is defined by the arrow diagram below.

Select the properties that accurately describe the following sequence with respect to graph G:⟨2,3,1,3,4⟩

 

A trail but not a path

A directed graph G has 5 vertices, numbered 1 through 5. The 5×5 matrix A is the adjacency matrix for G. The matrix A2 is given below.

Which vertex can be reached by a walk of length 4 that starts at vertex 1?

5

f:{0,1}4→{0,1}3f(x)

is obtained from x

by removing the first bit.

For example, f(1000)=000

.

Select the correct description of the function f

.

 

Onto but not one-to-one

f:{0,1}4→{0,1}4f(x)

is obtained by removing the second bit from x

and placing the bit at the end of the string. For example, f(1011)=1110

. Select the correct value for f−1(0101)

 

0110

The function f:{0,1}3→{0,1}3

is defined as:

For every x∈{0,1}2

, f(x)

is obtained by removing the first bit and adding a 1

to the end of the string.

For example, f(001)=011

.Select the set corresponding to the range of f.

 

{001,011,101,111}