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: No, we can't find a unique price for an apple and an orange.
Step-by-step explanation:
Since we have given that
Cost of 4 apples and 4 oranges = $10
Cost of 6 apples and 6 oranges = $12
We need to find the unique price for an apple and an orange.
According to question, our equations will be
![4x+4y=\$10\\\\6x+6y=\$12](https://tex.z-dn.net/?f=4x%2B4y%3D%5C%2410%5C%5C%5C%5C6x%2B6y%3D%5C%2412)
since it is equation of parallel lines, as
![\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{4}{4}=\frac{6}{6}\neq \frac{10}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_1%7D%7Ba_2%7D%3D%5Cfrac%7Bb_1%7D%7Bb_2%7D%5Cneq%20%5Cfrac%7Bc_1%7D%7Bc_2%7D%5C%5C%5C%5C%5Cfrac%7B4%7D%7B4%7D%3D%5Cfrac%7B6%7D%7B6%7D%5Cneq%20%5Cfrac%7B10%7D%7B12%7D)
Hence, No, we can't find a unique price for an apple and an orange.
Answer:
1. c; 2. d
Step-by-step explanation:
1. 2*3 = 6
2. (1.43*1000)p + (2.2*1000) = (-4.001*1000)
The answer should be 0.422
Based on the CPI, the expected price is
$12.75 * 193/100 = $24.61
The actual price is $28.50 -24.61 = $3.89 more than expected. The appropriate choice is ...
b. The actual price is $3.89 higher than the expected price.