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Anna35 [415]
2 years ago
14

I HAVE 1 MORE DAY TO TURN THIS IN SO HURRY

Mathematics
2 answers:
SCORPION-xisa [38]2 years ago
5 0

Hello there! I am EnjoyingLife, and I hope you find my answer helpful.

First of all, since all books cost less than $5, the most expensive a book could be is $4.99 (remember, less than, not less than or equal to)

Now, let's write an inequality to represent the cost of books.

We know that all books cost less than $5.

We have a sign for "less than". It's "<"

Thus,

p<5

Hope it helps!

Have an awesome day!

Good luck!

\rm{EnjoyingLife}

Misha Larkins [42]2 years ago
4 0

Answer:

a. What is the most expensive a book could be?

Answer : $ 4.99

b. Write an inequality to represent costs of books at sale.(use p as variable)

Answer : p < 5

hope that helps...

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Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar
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((a, b), (c, d))\in R

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1. First of all, let us check reflexive property:

Reflexive property means:

\forall a \in A \Rightarrow (a,a) \in R

Here we need to prove:

\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R

As per the given relation:

((a,b), (a,b) ) \Rightarrow ab =ab which is true.

\therefore R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R

Here we need to prove:

\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R

As per the given relation:

((a,b),(c,d)) \in R means ad = bc

((c,d),(a,b)) \in R means cb = da\ or\ ad =bc

Hence true.

\therefore R is symmetric.

3. R to be transitive, we need to prove:

if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R

((a,b),(c,d)) \in R means ad = cb.... (1)

((c,d), (e,f)) \in R means fc = ed ...... (2)

To prove:

To be ((a,b), (e,f)) \in R we need to prove: fa = be

Multiply (1) with (2):

adcf = bcde\\\Rightarrow fa = be

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0
3 years ago
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