Plz help me wit this

Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where (a

xxMikexx [17]

Answer:

a) R is reflexive, R is not symmetric, R is not anti-symmetric, R is transitive.

b) R is reflexive, R is symmetric, R is not anti-symmetric, R is not transitive.

c) R is not reflexive, R is symmetric, R is not anti-symmetric, R is not transitive.

Step-by-step explanation:

a)

(a, b) ∈ R if and only if everyone who has visited Web page a has also visited Web page b.

Obviously R is reflexive (aRa)

Everyone who has visited Web page a has also visited Web page a

R is not symmetric (aRb does not imply bRa)

If everyone who has visited Web page a has also visited Web page b does not mean that everyone who has visited Web page b has also visited Web page a

R is not anti-symmetric (aRb and bRa does not imply a=b)

If everyone who has visited Web page a has also visited Web page b and everyone who has visited Web page b has also visited Web page a does not mean the web pages are the same.

R is transitive (aRb and bRc implies aRc)

If everyone who has visited Web page a has also visited Web page b and everyone who has visited Web page b has also visited Web page c implies that everyone who has visited Web page a has also visited Web page c.

b)

(a, b) ∈ R if and only if there are no common links found on both Web page a and Web page b.

R is obviously reflexive (aRa)

R is symmetric (aRb implies bRa)

if there are no common links found on both Web page a and Web page b, then there are no common links found on both Web page b and Web page a.

R is not anti-symmetric (aRb and bRa does not imply a=b)

if there are no common links found on both Web page a and Web page b and there are no common links found on both Web page b and Web page a does not mean a and b are the same web page.

R is not transitive (aRb and bRc does not imply aRc)

Consider for example three web pages a, b and c such that a and c have a common link and b has no external links at all.

Then obviously (a,b)∈R and (b,c)∈R since b has no links, but (a,c)∉R because they have a common link.

c)

(a, b) ∈ R if and only if there is at least one common link on Web page a and Web page b

R is not reflexive

If the web page a does not have any link at all, then a is not related to a.

R is symmetric (aRb implies bRa)

if there is at least one common link found on Web page a and Web page b, then there is at least one common link found on Web page b and Web page a.

R is not anti-symmetric (aRb and bRa does not imply a=b)

if there is at least one common link found on Web page a and Web page b and there is at least one common link found on Web page b and Web page a does not mean the web pages are the same

R is not transitive (aRb and bRc does not imply aRc)

Consider for example three web pages a, b and c such that a has only two links L1 and L2, b has only two links L2 and L3 c has only two links L3 and L4.

Then (a, b) ∈ R since a and b have the common link L2, (b, c) ∈ R for b and c have the common link L3, but a and c have no common links, therefore (a,c)∉R

5 0

3 years ago

Square root of 9/16

Aleksandr-060686 [28]

$\sqrt{ \frac{9}{16} } = \frac{ \sqrt{9} }{ \sqrt{16} } = \frac{3}{4}$

5 0

3 years ago

a pelican. starts at 60 feet above sea level.it descends 60 feet to a catch fish. how do I explain it

goldenfox [79]

The pelican was at 60 feet above sea level, by descending 60 feet the pelican caught the fish at sea level.

8 0

3 years ago

Read 2 more answers

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible are possible

Vanyuwa [196]

Answer:

10

Step-by-step explanation:

5C2 =5!

2! (3)!

=1 x 2 x 3 x 4 x 5

(1 x 2) (1 x 2 x 3)

=4 x 5

2

=20

2

5C2 = 10

4 0

2 years ago

Can someone help we this and explain how to do it?

igomit [66]

Answer:

(0, 4) and (- 4, 0)

Step-by-step explanation:

We require the equation of the circle

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

The radius is the distance from the centre to a point on the circle

To calculate r use the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = ( $\sqrt{12}$ , - 2)

r = $\sqrt{((\sqrt{12 )^2 - 0)+(-2-0)^2} }$

= $\sqrt{12+4}$ = $\sqrt{16}$ = 4, hence

x² + y² = 16 ← equation of circle

given y - x = 4 ⇒ y = x + 4

Substitute y = x + 4 into the equation of the circle

x² + (x + 4)² = 16 → distribute and simplify left side

x² + x² + 8x + 16 = 16

2x² + 8x + 16 = 16 ( subtract 16 from both sides )

2x² + 8x = 0

2x(x + 4) = 0

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x + 4 = 0 ⇒ x = - 4

Substitute these values into y = x + 4 for corresponding y- coordinates

x = 0 : y = 4 ⇒ (0, 4)

x = - 4 : y = - 4 + 4 = 0 ⇒ (- 4, 0)

The points of intersection are (0, 4) and (- 4, 0)

8 0

3 years ago