They would be 8cm far apart.
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 .
To effectively determine the correct answer, it would be helpful to write this into an algebraic expression. We let x as the number. We do as follows:
<span>Four times the square of a certain number increased by 6 times the number equals 108.
4x^2 + 6x = 108
The numbers can be either of the following since the equation generated was a quadratic equation which has two roots.
x = 4.5
x = -6 </span>