1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dlinn [17]
3 years ago
15

Prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a un

iversal set U.
For or all sets A, B, and C, A∩(B−C) = (A∩ B)−(A∩C)

Hint: The statement is true. Sketch of proof: If x ∈ A∩(B−C), then x∈A and x∈B and x∉C. So it is true that x∈A and x∈B and that x∈A and x∉C.Conversely, if x ∈ (A∩ B)−(A∩C), then x∈A and x∈B, but x ∉ A∩C, and so x∉C.
Mathematics
1 answer:
tekilochka [14]3 years ago
5 0

Answer with Step-by-step explanation:

We are given that A, B and C are subsets of universal set U.

We have to prove that

A\cap (B-C)=(A\cap B)-(A\cap C)

Proof:

Let x\in A\cap (B-C)

Then x\in A and x\in(B-C)

When x\in ( B-C)then x\in B but x\notin C

Therefore, x\in( A\cap B) but x\notin (A\cap C)

Hence, it is true.

Conversely , Let x\in(A\cap B) but x\notin(A\cap C)

Then x\in A and x\in B

When x\notin ( A\cap C) then x\notin C

Therefor,x\in A\cap (B-C)

Hence, the statement is true.

You might be interested in
What is 18 divided by 82.8
astraxan [27]

Answer:

0.2173913043

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
On average, it takes a shoe factory 21 minutes, with a standard deviation of 3 minutes, to manufacture a pair of running shoes.
algol13

Answer:

The number of times it would take more than 27 minutes to manufacture a pair of running shoes is 2.275 times or approximately 2 times per every 100 shoes

Step-by-step explanation:

The average time it takes to manufacture a pair of shoes = 21 minutes;

The standard deviation = 3 minutes

To find how often it takes more than 27 minutes to manufacture a pair of running shoes, we have;

Standard score, given as follows;

Z=\dfrac{x-\mu }{\sigma }

Where;

x = The raw score = 27 minutes

μ = The average score = 21 minutes

σ = The standard deviation = 3 minutes

From which we have;

Z=\dfrac{27-21 }{3 } = 2

Therefore, it is borderline unusual with a p value of P(z>2) = 1 - 0.97725 = 0.02275

Therefore, the number of times out of 100 that it would take more than 27 minutes to manufacture a pair of running shoes = 100 × 0.02275 = 2.275 times which is approximately 2 times in every 100 shoes.

7 0
3 years ago
The explicit rule for an arithmetic sequence is f(n) = 7 + 4(n − 1).what are the fourth and fortieth terms?
vladimir1956 [14]
F(4) = 7+4(4-1)
f(4) = 7+4(3)
f(4) = 7+12
f(4) = 19
The forth term is 19 

f(40) = 7+4(40-1)
f(40) = 7+4(39)
f(40) = 7+156
f(40) = 163
The fortieth term is 163 
8 0
3 years ago
ANSWER ONLY IF YK IT IM GIVING CORRECT BRAINLIEST
wariber [46]

Answer:

-5(3x^3-1)

Step-by-step explanation:

-15x^3+5

Factor out -5

-5(3x^3-1)

4 0
3 years ago
If y varies directly as the square of x and Y = -54 when x = 9, then Y = -1
GarryVolchara [31]

Answer: false

Step-by-step explanation:

i just took the quiz and made a 60 so pls don’t be like me and fail it ;-;

6 0
3 years ago
Other questions:
  • 2 1/4 was subtracted twice from a number; then 1/8 was subtracted three times and 2/3 was subtracted twice. The resulting number
    10·1 answer
  • Simplify the expression.<br><br> (−5g5h6)2(g4h2)4
    6·2 answers
  • Please I need help with this problem number 5????
    10·1 answer
  • Which expressions are equivalent to 3x+3(x+y)3x+3(x+y)3, x, plus, 3, left parenthesis, x, plus, y, right parenthesis ? Choose al
    15·2 answers
  • If a fraction has<br> ____ in the denominator, it is undefined.
    12·2 answers
  • Express 0.7723 as a fraction
    13·2 answers
  • Melanie finds paint at the store for $4.95 per gallon. She also finds a Paintbrush for $3.75. Write an equation for y, the total
    10·2 answers
  • On her first shot, a golfer hit the ball 167167 yards. On her second shot, she hit the ball another 4949 feet and made it almost
    8·1 answer
  • Help please :)) Thanksss
    15·1 answer
  • #14 i
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!