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:
1
Step-by-step explanation:
that is the answer
because 51213÷3=17071
Answer:
perpendicular
Step-by-step explanation:
To determine if AB and CD are parallel, perpendicular, or neither, we need to get the slope of AB and CD first
Given A (−1, 3), B (0, 5),
Slope Mab = 5-3/0-(-1)
Mab = 2/1
Mab = 2
Slope of AB is 2
Given C (2, 1), D (6, −1)
Slope Mcd = -1-1/6-2
Mcd = -2/4
Mcd = -1/2
Slope of CD is -1/2
Take their product
Mab * Mcd = 2 * -1/2
Mab * Mcd = -1
Since the product of their slope is -1, hence AB and CD are perpendicular
Answer: The slope is: "3" ; which does not appear among the answer choices given.
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The slope, "m" is calculated as follows:
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Given two coordinates on a line;
m = (y₂ − y₁) / (x₂ − x₁) ;
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We are given the following 2 (TWO) coordinates:
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1) (5,2) ; which is: (x₁ ,y₁) ; so x₁ = 5 ; y₁ = 2 ; AND:
2) (7,8); which is: (x₂ ,y₂) ; so x₂ = 7; y₂ = 8 ;
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So; m = (y₂ − y₁) / (x₂ − x₁) = (8−2) /.(7−5) = 6/2 = 3 .
m = 3. The slope is: 3 ; which does not appear among the answer choices given.
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Alternately,
______________________________________________
We are given the following 2 (TWO) coordinates:
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1) (7,8) ; which is: (x₁ ,y₁) ; so x₁ = 7 ; y₁ = 8 ; AND:
2) (5,2); which is: (x₂ ,y₂) ; so x₂ = 5; y₂ = 2 ;
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So; m = (y₂ − y₁) / (x₂ − x₁) = (2−8) / (5−7) = -6/-2 = 3 .
m = 3. The slope is 3 ; which does not appear among the answer choices given.
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