Question

Determine whether the given statement is true or false. Explain your answer.

(a) If R is an antisymmetric relation, then R is not symmetric.

(b) If John Jay College was founded in 1997, then the moon is made of cheese. (

c) ∀x∃y(x divides y) where the domain of discourse for both variables is {2, 3, 4, 5, 6}.

(d) ∃x∀y(x divides y) where the domain of discourse for both variables is {2, 3, 4, 5, 6}.

(e) ∀n(3n ≤ 4n) where the domain of discourse is Z.

Answer #1

Determine whether the relation R is reflexive, symmetric,
antisymmetric, and/or transitive [4 Marks]
22
The relation R on Z where (?, ?) ∈ ? if ? = ? .
The relation R on the set of all subsets of {1, 2, 3, 4} where
SRT means S C T.

Determine whether the relation R on N is reﬂexive, symmetric,
and/or transitive. Prove your answer.
a)R = {(x,y) : x,y ∈N,2|x,2|y}.
b)R = {(x,y) : x,y ∈ A}. A = {1,2,3,4}
c)R = {(x,y) : x,y ∈N,x is even ,y is odd }.

Determine whether the given relation is an equivalence relation
on {1,2,3,4,5}. If the relation is an equivalence relation, list
the equivalence classes (x, y E {1, 2, 3, 4, 5}.)
{(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4),
(4,3)}
If the relation above is not an equivalence relation, state that
the relation is not an equivalence relation and why.
Example: "Not an equivalence relation. Relation is not
symmetric"
Remember to test all pairs in relation R

Use the table below to find the correlation coefficient and then
determine whether there is a linear relation between x and y. You
can use hand or calculator to find r this time.
x 0 5 7 8 9 y 3 8 6 9 4
A r = 0.4403, no there is no linear relation between x and y
B r = 0.3304, yes there is a linear relation between x and y
C r = 0.4403, yes there is...

True/False Questions.
For each question below, please answer “true” or “false” and
explain why. An answer without an explanation will result
in no credit.
2. (5 points) Max Gross has the utility function
U(x,y) =
max{x, y}. If the price of x
is the same as the price of y, Max will buy equal amounts
of x and y.
3. (5 points) Charlie’s utility function is
U(x,y) = xy^2. His
marginal rate of substitution between x and y
does not...

5. Determine whether the following statements are TRUE or FALSE.
If the statement is TRUE, then explain your reasoning. If the
statement is FALSE, then provide a counter-example. a) The
amplitude of f(x)=−2cos(X- π/2) is -2 b) The period of
g(x)=3tan(π/4 – 3x/4) is 4π/3.
. c) If limx→a f (x) does not
exist, and limx→a g(x) does not exist, then limx→a (f (x) + g(x))
does not exist. Hint: Perhaps consider the case where f and g are
piece-wise...

(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q)
→ ¬r are logically equivalent using either a truth table or laws of
logic.
(2) Let A, B and C be sets. If a is the proposition “x ∈ A”, b
is the proposition “x ∈ B” and
c is the proposition “x ∈ C”, write down a proposition involving a,
b and c that is logically equivalentto“x∈A∪(B−C)”.
(3) Consider the statement ∀x∃y¬P(x,y). Write down a...

Use the given transformation to evaluate the double integral.
(12x + 12y) dA R , where R is the parallelogram with vertices (−3,
6), (3, −6), (4, −5), and (−2, 7) ; x = 1/ 3 *(u + v), y = 1 /3* (v
− 2u)

explain why or not. Determine whther the ff statements are true
or not and give an explaination or counter example
1.The vector field F=<3X^2,1> is a gradient field for both
f(x,y)=x^3+y and f(x,y)=y+x^3+100
2.the vector field F=(y,x)/sqrt(x^2+y^2) is constant in
direction and magnitude on the unit circle.
3.the vector field F=(Y,X)/SQRT(X^2+Y^2) IS NEITHER RADICAL
FIELD NOR A ROTATION FIELD.explain
4.If a curve has a parametric description
r(t)=<x(t),y(t),z(t)>, whrer t is the arc length then
magnitude of r'(t)=1.explain
5.the vector field...

Use a scatterplot and the linear correlation coefficient r to
determine whether there is a correlation between the two variables.
Use alphaequals0.05. x 2 4 7 1 6 y 5 8 12 3 11 Click here to view a
table of critical values for the correlation coefficient.
LOADING... Does the given scatterplot suggest that there is a
linear correlation? A. Yes, because the data does not follow a
straight line. B. No, because the data follows a straight line. C....

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