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: f^{-1}(x) = 3-x/3
Step-by-step explanation: Let y = f(x) and rearrange making x the subject, that is...
1. y = - 3x + 3 ( add 3x to both sides )
2. 3x + y = 3 ( subtract y from both sides )
3. 3x = 3 - y ( divide both sides by 3 )
4. x = 3-y/3
Change x back into terms of y
f^{-1}(x) = 3-x/3
Answer:
on the x-axis
Step-by-step explanation:
it is located on the x axis because it is not technically in any quandrant. it is however, on an axis.
Answer:
The length of the segment F'G' is 7.
Step-by-step explanation:
From Linear Algebra we define reflection across the y-axis as follows:
, (Eq. 1)
In addition, we get this translation formula from the statement of the problem:
, (Eq. 2)
Where:
- Original point, dimensionless.
- Transformed point, dimensionless.
If we know that and , then we proceed to make all needed operations:
Translation
Reflection
Lastly, we calculate the length of the segment F'G' by Pythagorean Theorem:
The length of the segment F'G' is 7.
Answer:
60 percent i hope this helped.
Step-by-step explanation:
each have a a possibility of 10 and there's 6 of of 10 compared to 3 out of 10.