If A = {x, y, z} then the number of non-empty subsets of A is .

a) 8 b) 5 c) 6 d) 7​

(d) 7

Step-by-step explanation:

The total number of subsets that can be derived from a set with n elements is given by;

2ⁿ

Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;

2ⁿ - 1

Given:

A = {x, y, z}

Set A has 3 elements. This means that n = 3

Therefore, the total number of subsets that can be derived from set A is

2ⁿ = 2³ = 8

One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;

2ⁿ - 1 = 2³ - 1

8 - 1 = 7

This can be checked by writing all the possible subsets of A as follows;

∅

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Removing the empty set ∅, the non-empty subsets of A are;

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

idk

step-by-step explanation:

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~