Let W(x, y) mean that student x has visited website y, where the domain for x consists of all students in your school and the domain for y consists of all websites. Express each of these statements by a simple English sentence. ∃x∃y∀z((x ≠ y) ∧ (W(x, z) ↔ W(y, z)))

The statement can be expressed as

There are two different students in your class who have visited the same websites.

Step-by-step explanation:

Given that

- W(x, y) mean that student x has visited website y.

- The domain of x consists of all students in your school

- The domain of y consists of all website.

It would help to know the meaning of the symbols used, this will help understand the statement better.

- ∧ means conjuction

- ∃ means 'there exists'

- ∀ means 'for all'

- ≠ means 'different from'

- ↔ means 'if and only if'

The statement

∃x∃y∀z((x ≠ y) ∧ (W(x, z) ↔ W(y, z)))

can be expressed as:

There are two different students in your class who have visited the same websites.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer: 12x^2+6x

step-by-step explanation:

6x does not equal 24x. hope it works!