Mathematics, 29.07.2019 15:00 brianfranklin17

List all subsets of the following set: {dog, cat, fish}

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There are 8 subsets here. We have the original set {dog, cat, fish} which we can list the items in any order we want.

Then we have the set of items where we only pick two pets
{dog, cat}
{dog, fish}
{cat, fish}
the order for any given set does not matter

Then we have the set of just one pet only
{dog}
{cat}
{fish}

And finally, we have the empty set { } which is just curly braces with nothing inside.

In summary, we have these 8 subsets
{dog, cat, fish}
{dog, cat}, {dog, fish}, {cat, fish}
{dog}, {cat}, {fish}
{ }

Note how this is equal to 2^n = 2^3 = 8. The n = 3 indicates how many items are in the original set. The set of all possible subsets is known as the power set.

Answer from: jro20

Dog , cat
Dog , fish
Cat , fish
Dog, fish , cat
Fish, cat, dog
Cat, dog , fish
Fish , dog , cat

Answer from: Quest

d≈7.07in

step-by-step explanation:

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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