Which of the following is a valid conclusion based on the Venn diagram?

A.
If a pet is not a dog, then it is a beagle.
B.
If a pet is a dog, then it is a beagle.
C.
If a pet is a beagle, then it is a dog.
D.
If a pet is a dog, then it is not a beagle.

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:

2,5,8,11,14,17,20

Description: Each time there was an addition of 3 onto each 'y'.

Step-by-step explanation:

+3 to the last one each time

2+3=5

5+3=8 etc

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

Step-by-step explanation:

2 right 2 up

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:

9-8=1

7-(-6)=13

Step-by-step explanation:

you just add it the normal way.

Answer:

See below

Step-by-step explanation:

See following examples

a and b

a and -b

-a and b

-a and - b

Answer:

80

Step-by-step explanation:

8x+44-8x+36

8x-8x+44+36

44+36

80

9514 1404 393

Answer:

  C.  p ∨ q

Step-by-step explanation:

The compound statement is of the form ...

  p or q

where ...

  p = Memorial day is in July

  q = parallel lines intersect

The symbol ∨ is used to represent the disjunction (or).

The symbolic form of the given statement is ...

  p ∨ q

__

As it happens, both p and q are false, which means the disjunction is false. That has no bearing on the symbolic representation of it.

_____

∧ represents conjunction (and).

Answer:

0.25

Step-by-step explanation:

scale factor=md/od

=0.5/2

0.25

Answer: In point C.

Step-by-step explanation:

Plane ADB is the plane that contains the points A, D and B.

If you look in the image, you can see that point C also does belong to this plane.

Line EC is the line that connects the points E and C.

Now, remember that Point C does belong to the plane ADB, then the point where the plane ADB and line EC intersect is in point C, because it is a common point to both elements.

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:

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.

Answer:

28.08

Step-by-step explanation:

4(3+5)−3.92

Add 3 and 5 to get 8

4×8−3.92≈28.08

Multiply 4 and 8 to get 32

32−3.92≈28.08

Subtract 3.92 from 32 to get 28.08

28.08

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.

Step-by-step explanation:

1. use PEMDAS (Parentheses, Exponent, Multiplication & Division, Addition & Subtraction). you would do 3/4 divided by 3/8 first.

  3/4 / 3/8 = 2  

2. add 2 to -2 1/2 (or if it's easier to understand, do 2 minus 2 1/2)

  -2 1/2 + 2 = -1/2     OR       2- 2 1/2 = -1/2

answer is -1/2

Answer: the answer is y=9x

Step-by-step explanation:

Answer:

Addition Property of Equality If AB = CD then AB + BC = BC +CD

Subtraction Property of Equality If AB + BC = BC + CD then AB = CD

Multiplication Property of Equality If m∢A = 90 then 2(m∢A) = 180

Division Property of Equaliity If 2(m∢B) = 180 then m∢B = 90

Substitution Property If m∢A + m∢B =180 and m∢B then m∢A + 90 =180

Distributive Property AB + AB = 2AB

Reflexive Property m∢B = m∢B

Symmetric Property If AB + BC = AC then AC = AB + BC

Transitive Property If AB ≅ BC and BC ≅ CD then AB ≅ CD

Segment Addition Postulate If C is between B and D, then BC + CD = BD

Angle Addition Postulate If D is a point in the interior of ∢ABC then m∢ABD + m∢DBC = m∢ABC

Linear Pair Postulate If two angles form a linear pair, then they are supplementary

Definition of Right Angle If ∢B is a right angle then m∢B = 90

Definition of Midpoint If P is the midpoint of segment AB then AP =PB

Definition of Segment Bisector If k intersects segment AB at M the Midpoint then k bisects segment AB

Definition of Perpendicular Lines If two lines are ⊥ they form right angles

Definition of Congruent Segments If AB = CD then segment AB ≅ segment CD

Definition of Congruent Angles If ∡A ≅∡ B then m∡A=m∡B

Definition of Angle Bisector If ray AB bisects ∡CAD then∡ CAB ≅ ∡ BAD

Definition of Complementary Angles If ∡ Z and ∡Y are complementary m∡Z +m∡Y =90

Definition of Supplementary Angles If ∡ S and ∡T are supplementary m∡S +m∡T = 180

Step-by-step explanation:

Answer:

Answer A makes the most sense by far.  

Step-by-step explanation:

Answer A makes the most sense by far.   However, strictly speaking, the coefficient of x^2 does not have to be positive if we're using the quadratic formula.  Using some other approach, such as factoring, obtaining a positive coefficient for x^2 is helpful.

Answer:

Step-by-step explanation:

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Answer:

you can use an online graphing calculator

Step-by-step explanation:

Use the link in the screenshot

btw, the line after the word calculator is the cursor, so don't put anything after the word calculator.

Answer: X and Y

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

Answer:

Step-by-step explanation:

Answer:

m= -6

Step-by-step explanation:

Answer:

-16=m

Step-by-step explanation:

-3=-2+m/6

6*-3=-2+m*6

-18=-2+m

2+-18=m

-16=m

Answer:

18972 I use an calculator

The solution of number 527 × 36 after multiplying is,

⇒ 527 × 36 = 18,972

We have to give that,

To solve the expression,

⇒ 527 × 36

Now, simplify the numbers as,

⇒ 527 × 36

After multiply,

⇒ 18,972

So, the solution is,

⇒ 18,972

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ6

Answer:

it's A

Step-by-step explanation:

2x - 1

I put b and got it wrong

Answer:

no

Step-by-step explanation: pick up the phone baby i know your home

Answer:

the answer would be an equation