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iris [78.8K]
2 years ago
9

PLEASE HELP ME FAST

Mathematics
1 answer:
Ilya [14]2 years ago
8 0
1: AAS 2: SAS 3: AAS 4: SAS 5: not congruent 6: SSS
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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
Rachelle has $6.30 in nickels and quarters in her coin purse. The number of nickels is twice the number of quarters. How many co
timurjin [86]

Each group of 2 nickels and 1 quarter has a value of $0.35. Rachelle has $6.30/$0.35 = 18 such groups.

Rachelle has 18 quarters and 36 nickels.

5 0
2 years ago
Does this table represent a function? Why or why not?
Alina [70]

Answer: the answer is B

Step-by-step explanation:

7 0
2 years ago
If 2 straight lines intersect as shown, what is the value of z
Inessa [10]
You need to show the diagram
7 0
3 years ago
Pleqse help me do this thank you​
SpyIntel [72]

Answer:

84 grams; 5 ounces

Step-by-step explanation:

1oz = 28g

3*1oz = 3*28g

3 oz =  84g

140g = 5*28g = 5*1oz

140g = 5oz

5 0
3 years ago
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