How can you write 8⁴•7⁴ as a single power?

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

Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

$((a, b), (c, d))\in R$

Where $R$ is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

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

DELL LAPTOP WITH A RETAIL PRICE OF $525 FOR ONLY $393.75 what is the percent of change

Alex73 [517]

That is a 25% decrease.

8 0

3 years ago

Btw the answer needs to be a fraction.

VladimirAG [237]

Answer:

3/4

Step-by-step explanation:

7 0

3 years ago

If 1 skip equals 4 hops, and 1 jump equals 3 skips, what is the total number of hops in a hop, a skip and a jump

Aleksandr-060686 [28]

There are 17 hops in a hop, a skip, and a jump.

<h3></h3><h3>How to perform changes of units?</h3>

We have the relations:

1 skip = 4 hops.
1 jump = 3 skips.

How many hops are in a hop, a skip and a jump?

So we have:

1 hop + 1 skip + 1 jump.

First, using the second relation we rewrite:

1 hop + 1 skip + 3 skips = 1 hop + 4 skips.

Now, using the first relation:

1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.

There are 17 hops in a hop, a skip, and a jump.

If you want to learn more about changes of units:

brainly.com/question/9032119

#SPJ1

7 0

2 years ago

1 52/100 as a mixed number in decimal form

STatiana [176]

Answer:

I'm pretty sure its 1.52

6 0

3 years ago

Read 2 more answers