AnswersFL-1207350-Mathematics for College Liberal ArtsUnit Test

Unit Test — Unit test Answers

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1
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Let p: The day is Tuesday.Let q: The day is Thursday.Let r: She comes to work.Which represents the statement "The day is Tuesday or Thursday if and only if she comes to work”?

A
p ↔ (q ∧ r)
B
p ↔ (q ∨ r)
C
(p ∧ q) ↔ r
D
(p ∨ q) ↔ r
2
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Inductive and deductive reasoning differ in which way?

A
Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true.
B
Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.
C
Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true.
D
Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
3

Let p: A shape is a triangle.Let q: A shape has four sides.Which is true if the shape is a rectangle?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

Which is logically equivalent to the converse of a conditional statement?

A
the original conditional statement
B
the inverse of the original conditional statement
C
the contrapositive of the original conditional statement
D
the converse of the converse statement
6

Let p: The whole number has one digit.Let q: The whole number is less than 10.Which represents "The whole number has one digit if and only if the whole number is less than 10”?

A
p ∨ q
B
p ∧ q
C
p → q
D
p ↔ q
7

What is the converse of the statement?Perpendicular lines have negative reciprocal slopes.

A
If lines have negative reciprocal slopes, then they are perpendicular.
B
If lines are perpendicular, then they have negative reciprocal slopes.
C
If lines do not have negative reciprocal slopes, then they are not perpendicular.
D
If lines are not perpendicular, then they do not have negative reciprocal slopes.
8

Which statement can be concluded using the true statements?If a quadrilateral has 4 equal sides and 4 equal angles, then it is a square.If a figure is a square, then each of its angles must measure 90 degrees.

A
If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.
B
If a quadrilateral has 4 equal sides and 4 equal angles, then none of its angles measures 90 degrees.
C
If all four angles in a quadriateral measure 90 degrees, the quadrilateral is a square.
D
If all four angles in a quadriateral measure 90 degrees, the quadrilateral cannot be a square.
9

The truth table represents statements p, q, and r. pqr AT T T BT T F CT F T DT F F EF T T FF T F GF F T HF F F

A
r → (p ∧ q)
B
r → (p ∨ q)
C
(q ∧ r) → p
D
(q ∨ r) → p
10

2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.

Question illustration
A
I
B
II
C
III
D
IV
11

What value is a counterexample for the conditional statement shown?If a number between 0 and 100 is an odd perfect square, then the only factors of the number are 1, the number itself, and the square root of the number.

A
9
B
25
C
49
D
81
12

Circle B is inside of circle A.

Question illustration
A
A = {states in the US}; B = {world countries}
B
A = {plays by Shakespeare}; B = {playwrights}
C
A = {animals}; B = {mammals}
D
A = {polygons}; B = {circles}
13

Let p: The whole number has one digit.Let q: The whole number is less than 10.Which represents "The whole number has one digit if and only if the whole number is less than 10”?

A
p ∨ q
B
p ∧ q
C
p → q
D
p ↔ q
14

Consider the following sets.U = {all triangles}E = {x|x ∈ U and x is equilateral}I = {x|x ∈ U and x is isosceles}S = {x|x ∈ U and x is scalene}A = {x|x ∈ U and x is acute}O = {x|x ∈ U and x is obtuse}R = {x|x ∈ U and x is right}Which is a subset of I?

A
E
B
S
C
A
D
R

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