I need help with this question.

Can you help me with some steps to approach this proof .

Elis [28]

To prove two sets are equal, you have to show they are both subsets of one another.

• X ∩ (⋃ ) = ⋃ {X ∩ S | S ∈ }

Let x ∈ X ∩ (⋃ ). Then x ∈ X and x ∈ ⋃ . The latter means that x ∈ S for an arbitrary set S ∈ . So x ∈ X and x ∈ S, meaning x ∈ X ∩ S. That is enough to say that x ∈ ⋃ {X ∩ S | S ∈ }. So X ∩ (⋃ ) ⊆ ⋃ {X ∩ S | S ∈ }.

For the other direction, the proof is essentially the reverse. Let x ∈ ⋃ {X ∩ S | S ∈ }. Then x ∈ X ∩ S for some S ∈ , so that x ∈ X and x ∈ S. Because x ∈ S and S ∈ , we have that x ∈ ⋃ , and so x ∈ X ∩ (⋃ ). So ⋃ {X ∩ S | S ∈ } ⊆ X ∩ (⋃ ).

QED

• X ∪ (⋂ ) = ⋂ {X ∪ S | S ∈ }

Let x ∈ X ∪ (⋂ ). Then x ∈ X or x ∈ ⋂ . If x ∈ X, we're done because that would guarantee x ∈ X ∪ S for any set S, and hence x would belong to the intersection. If x ∈ ⋂ , then x ∈ S for all S ∈ , so that x ∈ X ∪ S for all S, and hence x is in the intersection. Therefore X ∪ (⋂ ) ⊆ ⋂ {X ∪ S | S ∈ }.

For the opposite direction, let x ∈ ⋂ {X ∪ S | S ∈ }. Then x ∈ X ∪ S for all S ∈ . So x ∈ X or x ∈ S for all S. If x ∈ X, we're done. If x ∈ S for all S ∈ , then x ∈ ⋂ , and we're done. So ⋂ {X ∪ S | S ∈ } ⊆ X ∪ (⋂ ).

QED

8 0

3 years ago

O 12 Ms. Ruby has 1 beanbag chair in her room. She lets 4 students take equal turns sitting in the chair during a 38-minute read

My name is Ann [436]

The number of students allowed to sit, N=4.

The total number of minutes, T=38 minutes.

Let x be the number of minutes for a student

$\begin{gathered} 4\text{ students-}\longrightarrow38\text{ minutes} \\ 1\text{ student--x} \\ \text{Cross multiplying,} \\ x=\frac{38\text{ minutes}}{4\text{ students}}\times1\text{ students} \\ =\frac{38}{4\text{ }}\text{minutes} \end{gathered}$

5 0

1 year ago

Twenty boys signed up for the school play. The number of girls who signed up was 195% of the number of boys. At the auditions, o

Firlakuza [10]

20 boys signed up
# of girls who signed up was 195% of the number of boys who signed up

Find 195% of 20:

1.95 * 20 = 39

So 39 girls signed up.

To find out what percent of girls who signed up for the play attended the auditions, divide 26 to the total number of girls who signed up:

26 / 39 = 0.666666667

Multiply by 100:

0.666666667 * 100 = 66.6666667%

So approximately 66.67% or 66 2/3%

7 0

4 years ago

Which is a solution to the equation |10-5y| = 20?

ioda

Answer:

{-2, 6}

Step-by-step explanation:

10-5y=20

-5y=10

y=-2

10-5y=-20

-5y=-30

y=6

6 0

3 years ago

NEED HELP WITH COFFEE QUESTION MASTERY GRADE !!

SVEN [57.7K]

Answer:

what are the opitions ?

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers