Question

Determine the truth value of each of the statement below. Explain your answer clearly.

(d) ∀x ∈ Z, ∃y ∈ R∗ ,(xy < 1)

(e) ∀(a, b) ∈ R × R, ∃(c, d) ∈ R × R,(ac = bd)

(f) ∀x ∈ R, ∃y ∈ R,(x + y = xy)

(g) ∃x ∈ R+, ∀x ∈ R+,(xy < y)

Answer #1

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 ≤...

Determine the truth value of each simple statement. Then using the
truth values, determine the truth value of the compound
statement.
1. If the moon circles the earth and the earth circles the sun, the
moon is made of cheese.
2. Honda makes automobiles or Honda makes motorcycles, if and only
if Mazda makes cereal.

Answer each of the questions below. (a) Find an equation for the
tangent line to the graph of y = (2x + 1)(2x 2 − x − 1) at the
point where x = 1. (b) Suppose that f(x) is a function with f(130)
= 46 and f 0 (130) = 1. Estimate f(125.5). (c) Use linear
approximation to approximate √3 8.1 as follows. Let f(x) = √3 x.
The equation of the tangent line to f(x) at x =...

3) The angles of a triangle are in a ratio of 1:1:2. Find the
ratio of the sides opposite these angles.
a) 1:1:2
b) 1:3‾√:2
c) Cannot be determined.
d) 1:1:2‾√
e) 2‾√:2‾√:1
f) None of the above
4)
Draw acute △ABC with m∠A=30∘. Draw altitude BD⎯⎯⎯⎯⎯⎯⎯⎯ from B
to AC⎯⎯⎯⎯⎯⎯⎯⎯. If BD=2, find AB.
a) 23‾√
b) 23‾√3
c) 43‾√3
d) 22‾√
e) 4
f) None of the above
5)
Assume that WZ=XY . Which of the following statements...

Let D = E = {−2, 0, 2, 3}. Write negations for each of the
following statements and determine which is true, the given
statement or its negation. Explain your answer
(i) ∃x ∈ D such that ∀y ∈ E, x + y = y.
(ii) ∀x ∈ D, ∃y ∈ E such that xy ≥ y.

Let D = E = {−2, 0, 2, 3}. Write negations for each of the
following statements and determine which is true, the given
statement or its negation. Explain your answer.
(i) ∃x ∈ D such that ∀y ∈ E, x + y = y.
(ii) ∀x ∈ D, ∃y ∈ E such that xy ≥ y.

10. Comparing Statements - Practice 2
Complete the truth table for the given propositions. Indicate
each proposition's main operator by typing a lowercase x in box
beneath the column in which it appears. On the right side of the
truth table, indicate whether each row lists identical or opposite
truth values for the two statements. Also indicate which, if any,
rows show that the statements are consistent with a lowercase x.
Finally, answer the questions beneath the truth table about...

For each of the following statements:
• Rewrite the symbolic sentence in words,
• Determine if the statement is true or false and justify your
answer,• Negate the statement (you may write the negation
symbolically).
√
(a) ∀x∈R, x2 =x.
(b) ∃y∈R,∀x∈R,xy=0.
(c) ∃x ∈ R, ∀y ∈ R, x2 + y2 > 9.

Philosophy
3. Multiple-Line Truth Functions
Compound statements in propositional logic are truth functional,
which means that their truth values are determined by the truth
values of their statement components. Because of this truth
functionality, it is possible to compute the truth value of a
compound proposition from a set of initial truth values for the
simple statement components that make up the compound statement,
combined with the truth table definitions of the five propositional
operators.
To compute the truth value...

For each of the following sets, determine whether they are
countable or uncountable (explain your reasoning). For countable
sets, provide some explicit counting scheme and list the first 20
elements according to your scheme. (a) The set [0, 1]R ×
[0, 1]R = {(x, y) | x, y ∈ R, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.
(b) The set [0, 1]Q × [0, 1]Q = {(x, y) |
x, y ∈ Q, 0 ≤ x ≤...

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