Which equation represents the circle shown on the graph below.

Prove the following DeMorgan's laws: if LaTeX: XX, LaTeX: AA and LaTeX: BB are sets and LaTeX: \{A_i: i\in I\} {Ai:i∈I} is a fam

MariettaO [177]

$X-(A\cup B)=(X-A)\cap(X-B)$

I'll assume the usual definition of set difference, $X-A=\{x\in X,x\not\in A\}$ .

Let $x\in X-(A\cup B)$ . Then $x\in X$ and $x\not\in(A\cup B)$ . If $x\not\in(A\cup B)$ , then $x\not\in A$ and $x\not\in B$ . This means $x\in X,x\not\in A$ and $x\in X,x\not\in B$ , so it follows that $x\in(X-A)\cap(X-B)$ . Hence $X-(A\cup B)\subset(X-A)\cap(X-B)$ .

Now let $x\in(X-A)\cap(X-B)$ . Then $x\in X-A$ and $x\in X-B$ . By definition of set difference, $x\in X,x\not\in A$ and $x\in X,x\not\in B$ . Since $x\not A,x\not\in B$ , we have $x\not\in(A\cup B)$ , and so $x\in X-(A\cup B)$ . Hence $(X-A)\cap(X-B)\subset X-(A\cup B)$ .

The two sets are subsets of one another, so they must be equal.

$X-\left(\bigcup\limits_{i\in I}A_i\right)=\bigcap\limits_{i\in I}(X-A_i)$

The proof of this is the same as above, you just have to indicate that membership, of lack thereof, holds for all indices $i\in I$ .

Proof of one direction for example:

Let $x\in X-\left(\bigcup\limits_{i\in I}A_i\right)$ . Then $x\in X$ and $x\not\in\bigcup\limits_{i\in I}A_i$ , which in turn means $x\not\in A_i$ for all $i\in I$ . This means $x\in X,x\not\in A_{i_1}$ , and $x\in X,x\not\in A_{i_2}$ , and so on, where $\{i_1,i_2,\ldots\}\subset I$ , for all $i\in I$ . This means $x\in X-A_{i_1}$ , and $x\in X-A_{i_2}$ , and so on, so $x\in\bigcap\limits_{i\in I}(X-A_i)$ . Hence $X-\left(\bigcup\limits_{i\in I}A_i\right)\subset\bigcap\limits_{i\in I}(X-A_i)$ .

4 0

3 years ago

ILL MARK YOU BRAINLIEST Factor completely 3ab(x + 1) − 2(x + 1).

Nuetrik [128]

Part one of answering how to factor

3 0

3 years ago

Can someone please help me ASAP

charle [14.2K]

Answer:

(4,12)

(-1,-3)

Step-by-step explanation:

x^2 - y = 4

y = 3x

Use substitution. Substitute 3x for y in the first equation

x^2 - (3x) = 4

x^2 -3x =4

Subtract 4 from each side

x^2 -3x -4 = 4-4

x^2 -3x-4 =0

Factor

(x-4) (x+1) =0

Using the zero product property

x-4 =0 x+1 =0

x=4 x=-1

Now to find y for each x solution

x=4

y =3x = 3(4) =12

(4,12)

x=-1

y =3x = 3(-1) =-3

(-1,-3)

4 0

3 years ago

Meredith's recipe for 2 1/2 dozen cupcakes calls for 3 cups of flour. She only has 1 cup of flour and needs to feed 12 people. C

oee [108]

I am pretty sure the awnser is yes because 2.5 divided by 3 equals .83 repeating which mean for one dozen of cupcakes(12) it would take .84 cups of flour.

7 0

2 years ago

How do you find the slope of the points: (19,-16),(-7,-15)?

nirvana33 [79]

Answer:

$\Huge\boxed{\mathsf{\frac{1}{26} }}$