Answers FL-1207350-Mathematics for College Liberal ArtsUnit Test

Unit Test — Unit test Answers

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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”?

p ↔ (q ∧ r)

p ↔ (q ∨ r)

(p ∧ q) ↔ r

(p ∨ q) ↔ r

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Inductive and deductive reasoning differ in which way?

Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true.

Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.

Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true.

Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.

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

Option

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

the original conditional statement

the inverse of the original conditional statement

the contrapositive of the original conditional statement

the converse of the converse statement

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”?

p ∨ q

p ∧ q

p → q

p ↔ q

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

If lines have negative reciprocal slopes, then they are perpendicular.

If lines are perpendicular, then they have negative reciprocal slopes.

If lines do not have negative reciprocal slopes, then they are not perpendicular.

If lines are not perpendicular, then they do not have negative reciprocal slopes.

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.

If a quadrilateral has 4 equal sides and 4 equal angles, then each of its angles must measure 90 degrees.

If a quadrilateral has 4 equal sides and 4 equal angles, then none of its angles measures 90 degrees.

If all four angles in a quadriateral measure 90 degrees, the quadrilateral is a square.

If all four angles in a quadriateral measure 90 degrees, the quadrilateral cannot be a square.

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

r → (p ∧ q)

r → (p ∨ q)

(q ∧ r) → p

(q ∨ r) → p

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.

III

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.

Circle B is inside of circle A.

A = {states in the US}; B = {world countries}

A = {plays by Shakespeare}; B = {playwrights}

A = {animals}; B = {mammals}

A = {polygons}; B = {circles}

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”?

p ∨ q

p ∧ q

p → q

p ↔ q

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?