Answer:
See answer below
Step-by-step explanation:
The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.
i) x∈AnB if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.
ii) (I will abbreviate "if and only if" as "iff")
x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.
iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).
iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).
n
y
=
−
x
−
4
To find the x-intercept, substitute in
0
for
y
and solve for
x
.
0
=
−
x
−
4
Solve the equa
−
x
−
4
=
0
.
−
x
−
4
=
0
Add
4
to both sides of the equation.
−
x
=
4
Multiply each term in
x
=
−
4
by
−
1
x
=
−
4
To find the y-intercept, substitute in
0
for
x
and solve for
y
.
y
=
−
(
0
)
−
4
Simplify
−
(
0
)
−
4
.
Multiply
−
1
by
0
.
y
=
0
−
4
Subtract
4
from
0
.
y
=
−
4
These are the
x
and
y
intercepts of the equation
y
=
−
x
−
4
.
x-intercept:
(
−
4
,
0
)
y-intercept:
(
0
,
−
4
)
not too sure
X has infinity solutions.
They already spent $2000, and they only had $5100
Subtract
5100 - 2000 = 3100
$3,050 is your answer, because it is the only one that is less than 3100
hope this helps
Answer:
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle
