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Fiesta28 [93]
3 years ago
6

Find AB, BC, and AC

Mathematics
1 answer:
sp2606 [1]3 years ago
4 0
This algebra one or two please mark me brainlist I need 1
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(a) Let R = {(a,b): a² + 3b <= 12, a, b € z+} be a relation defined on z+)
grin007 [14]

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

4 0
2 years ago
If Sally has 4 apples and she gives away two then collects 11 then gives away 4 again and her friend has 6 grapes and gives sall
Rina8888 [55]
There are 12 pieces of fruit in total
8 0
3 years ago
Matt is a quarterback on the local football team. In the first quarter, Matt threw eight passes. Three passes were completions f
olganol [36]

Answer:

I think it's 28 yards gained.

Step-by-step explanation:

12 + 17 + 6 = 35

2 + 5 = 7

35 - 7 = 28

Please tell me if I'm wrong

6 0
3 years ago
If you can read this please answer it
Harlamova29_29 [7]
Indirect proportion:   y = k/x.

Here, y = 2 / (3x); x is in the denominator of the fraction.  Thus, this equation does represent indirect proportion, with k = (2/3).

       2/3
y = -------
         x
6 0
3 years ago
Which pairs of expressions are equivalent?<br> Quick
stiks02 [169]

Answer:

a

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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