Answer:
isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.
Step-by-step explanation:
Let 
denote a set of elements. 
would denote the set of all ordered pairs of elements of 
.
For example, with 
, 
and 
are both members of . However, 
because the pairs are ordered.
A relation on is a subset of . For any two elements
, 
if and only if the ordered pair 
is in 
.
A relation on set is an equivalence relation if it satisfies the following:
- Reflexivity: for any
, the relation needs to ensure that 
(that is: 
.)
- Symmetry: for any , if and only if
. In other words, either both and 
are in , or neither is in .
- Transitivity: for any
, if and 
, then 
. In other words, if and 
are both in , then 
also needs to be in .
The relation (on ) in this question is indeed reflexive. 
, 
, and 
(one pair for each element of ) are all elements of .
isn't symmetric. 
but 
(the pairs in 
are all ordered.) In other words, 
isn't equivalent to 
under even though 
.
Neither is transitive. 
and 
. However, . In other words, under relation , 
and 
does not imply 
.
Answer:
um
Step-by-step explanation:
The height of a tree is 10
10
meters long and it grows 1
1
cm in a year.
Then its height after one year = 10
10
meters 1
1
cm
Its height after 3
3
years = 10
10
meters 3
3
cm
Its height after 6
6
years = 10
10
meters 6
6
cm
Its height after x
x
years = 10
10
meters x
x
cm
Where x
x
represents an unknown number. From the last line, we can find height of the tree after a certain number of years by taking x
x
equal to that number. For example, we simply let x=15
x
=
15
, 25
25
and 55
55
. Thus, the value of x
x
depends on our choice. We can give x
x
any value or number we want. In other words, the value of x
x
is not fixed, it varies from one situation to the other. Therefore, we call x
x
a variable whereas 10
10
is a fixed number whole value does not change. So 10
10
therefore is called a constant.
Read more: http://www.emathzone.com/tutorials/basic-algebra/algebraic-expression.html#ixzz4fDkFcbpZ
Answer:
Las Vegas
Step-by-step explanation:
We are given the dimensions 10 feet length and 3 inches height. The volume of the rectangular portion is equal to $72.59 / $98 per cubic yard that is equal to 0.74 cubic yard. This is equal to 19.98 cubic feet. This means the width of the portion is equal to 8 feet.
