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
DaniilM [7]
2 years ago
9

Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .

Mathematics
1 answer:
adelina 88 [10]2 years ago
3 0

Solution :

We have to prove that $\overline{A \cup B} = \overline{A} \cap \overline{B}$   (De-Morgan's law)

Let  $x \in \bar{A} \cap \bar{B}, $ then $x \in \bar{A}$ and $x \in \bar{B} $

and so $x \notin \bar{A}$ and $x \notin \bar{B} $.

Thus, $x \notin A \cup B$ and so $x \in \overline{A \cup B}$

Hence, $\bar{A} \cap \bar{B} \subset \overline{A \cup B}$   .........(1)

Now we will show that $\overline{A \cup B} \subset \overline{A} \cap \overline{B}$

Let $x \in \overline{A \cup B}$ ⇒ $x \notin A \cup B$

Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.

$x \in \overline{A}$ and  $x \in \overline{B}$

Therefore, $x \in \overline{A} \cap \overline{B}$ and we have $\overline{A \cup B} \subset \overline{A} \cap \overline{B}$  .............(2)

From (1) and (2),

$\overline{A \cup B} = \overline{A} \cap \overline{B}$

Hence proved.

You might be interested in
If 6x -1 = 29, what is the value of x² + x?
irina1246 [14]

Answer: <em>The answer would be x (x+1)</em>

7 0
3 years ago
Read 2 more answers
1.Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.
sleet_krkn [62]
I´m sure that the answer is 96cm^2, because the area of the triangles is 18 and 6 and the area of the rectangle is 72.
5 0
3 years ago
BRAINLIEST ASAP! PLEASE HELP ME :)
WITCHER [35]

Answer:

sin⁴x - sin²x

sin²x(sin²x - 1)

(1 - cos²x)(1 - cos²x - 1)

(1 - cos²x)(-cos²x)

-cos²x + cos⁴x

cos⁴x - cos²x

4 0
3 years ago
Consider the equation 2y - 4x = 12
Aleks [24]

Answer:

y = 2x + 6 and 2y-4x=12 are the same line, so have infinitely many solutions.

Step-by-step explanation:

2y - 4x = 12

This is the same as y = 2x + 6

4 0
2 years ago
Read 2 more answers
8b + 4 - 4b + 2 = <br><br> A) 12b + 6 <br> B) 4b^2 ​2 ​​ + 4 + 2 <br> C) 12bb + 6 <br> D) 4b + 6
trapecia [35]
<h2>Answer:</h2><h2>D. 4b + 6</h2><h2 /><h2>Hope this helps!!</h2>

5 0
2 years ago
Read 2 more answers
Other questions:
  • Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi
    15·1 answer
  • The lengths of the perpendiculars drawn to the sides of a regular hexagon from an interior point are 4, 5, 6, 8, 9, and 10 centi
    12·1 answer
  • 7x + 3 = 10x - 5.4<br><br> will mark brainliest u do not have to show work
    6·2 answers
  • If cos 65 degree +cos 55 degree = cos θ, find θ in radians
    10·1 answer
  • How do you solve equations that contain like terms
    13·2 answers
  • Please help me asap thank you!
    10·2 answers
  • What is y = -2x +4, x =3.5​
    11·1 answer
  • Round each number to the nearest 100 <br> 976
    9·2 answers
  • Please Help, I don't understand how I get one of the answers below
    10·1 answer
  • What is the volume of the following triangular prism?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!