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DaniilM [7]
3 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]3 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.

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A point on the terminal side of an acute angle in standard position is (1, 2 √2). Find the cosine value of this angle.
kozerog [31]

Answer:

cos\theta=1/3

Step-by-step explanation:

The point at the terminal side of an acute angle is given by (1, 2\sqrt{2} ).

That is,

x = 1 and y= 2\sqrt{2} .

Let r be the length of line segment drawn from the origin to the point and is given by the formula:

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Substituting the values of x and y into r,

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r = \sqrt{1 + 8}

r = \sqrt{9}

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4 0
3 years ago
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STatiana [176]

Answer:

N=N so b

Step-by-step explanation:

Because in LN=NP the reflexive property essentially takes this info and repeats itself N=N

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3 years ago
When using order of operations to simplify expressions
Semmy [17]
What’s the question?
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RideAnS [48]
Since the number of members attending is 40, you can eliminate 17 as a possible answer, as it is smaller than 40. You can also eliminate 240 because 40 members is 60%, so the answer must be less than 80. You are now left with 67 and 73. 

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Pls help to get the answer
soldier1979 [14.2K]
When they say quotient, they want a fraction, so the answer for that would be
\frac{6}{10}
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