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stiks02 [169]
3 years ago
14

Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅, {∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅, {∅}} f

) {{∅}} ⊂ {∅, {∅}} g) {{∅}} ⊂ {{∅}, {∅}}
Mathematics
1 answer:
Nina [5.8K]3 years ago
7 0

Answer:

a) True

b) True

c) False

d) True

e) True

f) True

g) True

Step-by-step explanation:

Let A be a set. a belongs (is element of) to A if and only if a∈A.

a) The only element of {∅} is ∅, thus ∅∈{∅}.

b) The elements of {∅, {∅}}  are ∅ and {∅}, hence ∅ ∈ {∅, {∅}}.

c) The only element of {∅} is ∅. We have that {∅}≠∅ because {∅} has one element but ∅ has 0 elements. Therefore, {∅} ∉ {∅}, since {∅} is not an element of {∅}.

d) The only element of {{∅}} is {∅}. Hence {∅} ∈ {{∅}}.

e) The elements of {∅, {∅}} are ∅ and {∅}. The only element of {∅} is ∅. Then, every element of {∅} is also an element of {∅, {∅}}. That is, {∅} ⊂ {∅, {∅}}.

f) The elements of {∅, {∅}} are ∅ and {∅}. The only element of {{∅}} is {∅}. Then, every element of {{∅}} is also an element of {∅, {∅}}. That is, {{∅}} ⊂ {∅, {∅}}.

g) The only element of {{∅}, {∅}}={{∅}} is {∅}. The only element of {{∅}} is {∅}. Then, every element of {{∅}} is also an element of {{∅}}. That is, {{∅}} ⊂ {{∅}, {∅}}={{∅}}.

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Answer:

Base = 24 cm or 10cm

Step-by-step explanation:

REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²

Using the formulas

A=\frac{bh_b}{2}

h_b=\sqrt{a^2-\frac{b^2}{4} }

There are 2 solutions for b

b=2\sqrt{2}   \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2+\sqrt{13^4-4*60^2} } } ≈ 10cmb=2\sqrt{2}   \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2-\sqrt{13^4-4*60^2} } }=24cm

Less complex:

Area of a triangle = 1/2 * b * h = 60

=> h = 120/b

In right triangle ABD

13² = h² + b² /4 ( by Pythagoras law)

=>169 = 120²/b² + b²/4

=>676 b² = 57600 + b^4

=> b^4 - 676 b² + 57600 = 0

=> b² = 676 +- √(676² - 4*57600) / 2

=> b²= 676 +- √(226576) /2

=> b² = (676 +- 476 )/2

=> b² = 1152/2 , 200 /2

=> b² = 576 , 100

=> b = 24, 10

So, Base = 24 cm or 10cm

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2 years ago
A new park was designed to contain two circular gardens. Garden A had a diameter 50 m, anf garden B has a diameter of 70 m. If t
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\qquad\qquad\huge\underline{{\sf Answer}}

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2 years ago
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Answer:

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Step-by-step explanation:

Well, the answer is 2.

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Answer:

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