What is the function equation of this table?

Answer:

(a) and (b) are not true in general. Refer to the explanations below for counterexamples.

It can be shown that (c) is indeed true.

Step-by-step explanation:

This explanation will use a lot of empty sets [tex]\phi[/tex] just to keep the counterexamples simple.

Note that [tex]A \cap B[/tex] can well be smaller than [tex]A[/tex]. It should be alarming that the question is claiming [tex]A\![/tex] to be a subset of something that can be smaller than [tex]\! A[/tex]. Here's a counterexample that dramatize this observation:

Consider:

The intersection of an empty set with another set should still be an empty set:

[tex]A \cap B = \left\lbrace 1\right\rbrace \cap \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].

The union of two empty sets should also be an empty set:

[tex]((A \cap B) \cup C) = \left\lbrace\right\rbrace \cup \left\lbrace\right\rbrace = \left\lbrace\right\rbrace[/tex].

Apparently, the one-element set [tex]A = \left\lbrace 1 \right\rbrace[/tex] isn't a subset of an empty set. [tex]A \not \subseteq ((A\cap B) \cup C)[/tex]. Contradiction.

Consider the same counterexample

Left-hand side:

[tex](A \cup B) \cap C = \left(\left\lbrace 1 \right\rbrace \cup \left\lbrace \right\rbrace\right) \cap \left\lbrace 2 \right\rbrace\right = \left\lbrace 1 \right\rbrace \cap \left\lbrace 2 \right\rbrace = \left\lbrace \right\rbrace[/tex].

Right-hand side:

[tex](A \cap B) \cup C = \left(\left\lbrace 1 \right\rbrace \cap \left\lbrace \right\rbrace\right) \cup \left\lbrace 2 \right\rbrace\right = \left\lbrace \right\rbrace \cup \left\lbrace 2 \right\rbrace = \left\lbrace 2 \right\rbrace[/tex].

Apparently, the empty set on the left-hand side [tex]\left\lbrace \right\rbrace[/tex] is not the same as the [tex]\left\lbrace 2 \right\rbrace[/tex] on the right-hand side. Contradiction.

Part one: show that left-hand side is a subset of the right-hand side.

Let [tex]x[/tex] be a member of the set on the left-hand side.

[tex]x \in (A \backslash B) \cap C[/tex].

[tex]\implies x\in A \backslash B[/tex] and [tex]x \in C[/tex] (the right arrow here reads "implies".)

[tex]\implies x \in A[/tex] and [tex]x \not\in B[/tex] and [tex]x \in C[/tex].

[tex]\implies (x \in A\cap C)[/tex] and [tex]x \not\in B \cap C[/tex].

[tex]\implies x \in (A \cap C) \backslash (B \cap C)[/tex].

Note that [tex]x \in (A \backslash B) \cap C[/tex] (set on the left-hand side) implies that [tex]x \in (A \cap C) \backslash (B \cap C)[/tex] (set on the right-hand side.)

Therefore:

[tex](A \backslash B) \cap C \subseteq (A \cap C) \backslash (B \cap C)[/tex].

Part two: show that the right-hand side is a subset of the left-hand side. This part is slightly more involved than the first part.

Let [tex]x[/tex] be a member of the set on the right-hand side.

[tex]x \in (A \cap C) \backslash (B \cap C)[/tex].

[tex]\implies x \in A \cap C[/tex] and [tex]x \not\in B \cap C[/tex].

Note that [tex]x \not\in B \cap C[/tex] is equivalent to:

However, [tex]x \in A \cap C[/tex] implies that [tex]x \in A[/tex] AND [tex]x \in C[/tex].

The fact that [tex]x \in C[/tex] means that the only possibility that [tex]x \not\in B \cap C[/tex] is [tex]x \not \in B[/tex].

To reiterate: if [tex]x \not \in C[/tex], then the assumption that [tex]x \in A \cap C[/tex] would not be true any more. Therefore, the only possibility is that [tex]x \not \in B[/tex].

Therefore, [tex]x \in (A \backslash B)\cap C[/tex].

In other words, [tex]x \in (A \cap C) \backslash (B \cap C) \implies x \in (A \backslash B)\cap C[/tex].

[tex](A \cap C) \backslash (B \cap C) \subseteq (A \backslash B)\cap C[/tex].

Combine these two parts to obtain: [tex](A \backslash B) \cap C = (A \cap C) \backslash (B \cap C)[/tex].

Answer:

A,B,C,D

Step-by-step explanation:

They are all the same equation on both sides of the equal sign and sense the variable is x on all of them whatever number you put on one side you have to put it on the other side therefore resulting in any solution you could think of.

Answer:

9 × 9 = 81

This is basic 12x12 tables math

Answer:

81

Step-by-step explanation:

you just take 9 and times it by 8 and you get 81

Answer:

0.25

Step-by-step explanation:

scale factor=md/od

=0.5/2

0.25

Applying the HL congruence theorem, the information marked in the diagram cannot be congruent, so it is FALSE.

The HL congruence theorem states that if the corresponding legs of two right traingles are congruent, and the their hypotenuse are also congruent, then the triangles are congruent.

From the information given, we are not told if the hypotenuse of the right triangles are congruent, so we can't apply the HL congruence theorem to prove they are congruent. The answer is FALSE.

Learn more about the HL congruence theorem on:

https://brainly.com/question/2102943

Answer:

4.543 billion years i think, i apologize if im wrong

Step-by-step explanation:

Answer:

4.54 billion years

Step-by-step explanation:

Scientists use the layers of rock of the Earth's crust/core to estimate how old is the earth.

[tex]8x + 40 = 120[/tex]

Subtract sides -40

[tex]8x + 40 - 40 = 120 - 40[/tex]

[tex]8x = 80[/tex]

Divided sides by 8

[tex] \frac{8}{8}x = \frac{80}{8} \\ [/tex]

[tex]x = 10[/tex]

Done .....♥️♥️♥️♥️♥️

x+2

Step-by-step explanation:

x+2

If x = –2 is a zero, then x + 2 = 0, so x + 2 is a factor. Similarly, if x = 1/3 is a zero, then x – 1/3 = 0, so x – 1/3 is a factor. By giving me two of the zeroes, they have also given me two factors: x + 2 and x – 1/3.

Answer:

i think it is -1/2

Answer:

[tex] -\dfrac{13}{18} [/tex]

Step-by-step explanation:

[tex] -\dfrac{8}{9} - (-\dfrac{1}{6}) = [/tex]

[tex] = -\dfrac{8}{9} + \dfrac{1}{6} [/tex]

[tex] = -\dfrac{16}{18} + \dfrac{3}{18} [/tex]

[tex] = -\dfrac{13}{18} [/tex]

Answer:

Letter B is yes because if you use the vertical line test, never anytime the vertical line intersect the graph in more than one point.

Answer: If ∡PQR = 82°, and the ray QS bisects it, it cuts ∡PQR into two equal halves, ∡PQS and ∡RQS, each of which is then 82/2, or 41°.

Answer:

16.825 is the answer for your question

Answer:

Step-by-step explanation:

Answer:

Did you mean [tex]\frac{-2x}{9} ?\\[/tex]

Please clarify so that I can work this problem out for you :)

Step-by-step explanation:

Answer:

Multiply 5 by 4.22 because 5 cups of water is 4.22 liters

Answer:

Step-by-step explanation:

3(3z-6)=0

multiply your three with the 3z and the -6

9z-18=0

figure out what - 18 = 0

9z=18

9*2=18

z=2

hope this helps

Answer

7 weeks

Step-by-step explanation:

$490 - $175 = $315

John needs $315 still for the camera

divdie $315 by $50 and you get 6.3 but because it cant be 6 weeks he would be short $15 you would have to wait an additional week in order to cover the cost of the camera completly.

Brainliest please!!!!

Answer:

1) 122°

2) 58°

3) 60°

4) 120°

5) 58°

6) 62°

7) 60°

8) 58°

9) 62°

10) 60°

11) 58°

12) 122°

13) 120°

14) 60°

15) 62°

16) 58°

17) 122°

18) 122°

19) 58°

Step-by-step explanation:

Basically Angle Relationships

Each Angle all matches to a different Angle due to their same degree. It is kind of confusing at first but really easy when you understand it and look at it with pacience.

This took so long lol. I really hope it helps! :D

Answer: X and Y

Step-by-step explanation: IF I REMEMBER dont get mad if you don’t get it right

Answer:

y=9/2x -13/2

Step-by-step explanation:

i used a calculator i hope its right

Answer: it would be 2 to the right and 2 up

Step-by-step explanation:

2 right 2 up

Answer:

Alyssa needs 1056 cubed feet of wallpaper.

Step-by-step explanation:

Its just 12 times 11 times 8 to find the volume.

Answer:

257890 is the function of the equation

Step-by-step explanation:

mark me BRAINLIEST

Answer:

it's A

Step-by-step explanation:

2x - 1

I put b and got it wrong