Question

List all element of the following sets

a. { 1/n ∣ n ∈ { 3 , 4 , 5 , 6 } }

b. {x∈Z ∣ x=x+1}

c. {n∈P ∣ n is a factor of 24 }

Answer 1

Answer:  The elements of the given sets are listed below.

Step-by-step explanation:  We are given to list the elements of the following sets :

$(a)~\left\{\dfrac{1}{n}:n\in \{3,4,5,6\}\right\},\\\\\\(b)~\{x\in \mathbb{Z}|x=x+1\},\\\\\\(c)~\{n\in P|\textup{n is a factor of 24}\}.$

The listing of the elements of the given sets is done below :

$(a)~\left\{\dfrac{1}{n}:n\in \{3,4,5,6\}\right\}.$

Here, the elements of the set will be the reciprocal of 3, 4, 5 and 6.

So, the list of elements of the set is

$\left\{\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},\dfrac{1}{6}\right\}.$

$(b)~\{x\in \mathbb{Z}|x=x+1\}.$

For x to be an element of this set, we have

$x=x+1\\\\\Rightarrow 0=1,$ which is NEVER possible. So, the given set is empty.

That is, $\{x\in \mathbb{Z}|x=x+1\}=\phi.$

$(c)~\{n\in P|\textup{n is a factor of 24}\}.$

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Since we need prime factors, so the elements of the given set are

$\{2,3\}.$

Thus, all the elements of the given sets are listed.