Question

- 8. The set in roster form C = {x: x is a factors of 8xy) : .......

9. D = (7.49, 343, 2401) in the set builder form.​

Answer 1

8. We have to find the set C = {x : x is a factor of 8xy} in roster form.

Here x and y are some variables so we can't guarantee a definite value for them. They're some integers, but we can't say either they're prime or composite, both can be too, but won't be definite.

But here we just assume that x and y are prime numbers.

Because we want them not to be split!

So, as just prime factorization, we can write 8xy = 2³ · x¹ · y¹.

(If both were considered as composites, they would be assumed to be split as product of some primes, but it won't be definite too. Because we can't predict x and y should be split as product of how many prime numbers!!!)

Now, to find the no. of factors, just add 1 to each of the exponents of the factors in the factorization, and then multiply the three.

I.e., (3 + 1)(1 + 1)(1 + 1) = 4 · 2 · 2 = 16

So there are 16 factors for 8xy.

Which may be they?!

They're written in roster form as below:

C = {1, 2, 4, 8, x, 2x, 4x, 8x, y, 2y, 4y, 8y, xy, 2xy, 4xy, 8xy}

So this is the answer!

9. Given set is D = {7, 49, 343, 2401}.

The elements in the set are actually the first four consecutive powers of 7.

7¹ = 7 ; 7² = 49 ; 7³ = 343 ; 7⁴ = 2401

So each elements are in the form 7ⁿ.

Here n is a natural number and n can have values 1, 2, 3, 4 only, i.e., n ≤ 4.

So the set D in set builder form is,

$D=\{x:x=7^n,\ n\in\mathbb{N},\ n\leq 4\}$