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2 years ago

11

The temperature in St. Louis, Missouri, is 31°F. The temperature in Duluth, Minnesota, is -29°F. Is the temperature in St. Louis

or Duluth closer to 0°F?

1 answer:

Sati [7]2 years ago

3 0

-29 is 29 degrees away from 0 degrees.

31 is 31 degrees away from 0 degrees.

-29 (the temperature in Duluth) is closer to 0, because 29 is less than 31.

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Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф

asambeis [7]

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = (A ∩ B) (Addition to zero identity property)

∴ A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅ ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

4 0

3 years ago

The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (

Mamont248 [21]

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

$x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm$

Let the total length of the 9 adults' big finger = T

$x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm$

The total length of the 13 people's big finger = t + T

= 56 + 144.9

=200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

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