Answers OC27 MATH COLL LIB ARTS-1207350-S2-Maguire-DAquinoUnit Test

Unit 1 TEST: Sets and Logic Answers

25 verified answers2 views

Free Preview

Which disjunction is always true for any real number x?

A number, x, is less than 0 or greater than 1.

A number, x, is less than 0 or greater than 0.

A number, x, is greater than 5 or less than 10.

A number, x, is greater than 5 or less than 1.

Free Preview

Given:p: Two linear functions have different coefficients of x.q: The graphs of two functions intersect at exactly one point. Which statement is logically equivalent to q → p?

If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.

If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.

If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same coefficients of x.

If the graphs of two functions intersect at exactly one point, then the two linear functions have the same coefficients of x.

Branden and Janna are analyzing the same conditional statement. Branden finds multiple examples that validate the conditional statement. Janna finds one example that satisfies the hypothesis of the conditional statement, but not the conclusion. Which must be true?

The conditional statement is true. There are more examples that validate the statement than there are that do not.

The conditional statement is true. There is at least one example that validates the statement.

The conditional statement is false. There is at least one counterexample for the statement.

The conditional statement is false. There must be exactly one example that validates the statement.

Given:p: 2x = 16q: 3x – 4 = 20Which is the converse of p → q?

If 2x ≠ 16, then 3x – 4 ≠ 20.

If 3x – 4 ≠ 20, then 2x ≠ 16.

If 2x = 16, then 3x – 4 = 20.

If 3x – 4 = 20, then 2x = 16.

Which disjunction is always true for any real number x?

A number, x, is less than 0 or greater than 1.

A number, x, is less than 0 or greater than 0.

A number, x, is greater than 5 or less than 10.

A number, x, is greater than 5 or less than 1.

What is the inverse of the conditional statement?If a polygon has five angles, then it is a pentagon.

If a polygon is a pentagon, then it has five angles.

If a polygon is not a pentagon, then it does not have five angles.

If a polygon does not have five angles, then it is not a pentagon.

If a polygon has five angles, then it is not a pentagon.

Let p: The shape is a rhombus.Let q: The diagonals are perpendicular.Let r: The sides are congruent.Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

p ∧ (q ∧ r)

(p ∨ q) ∨ r

p ↔ (q ∧ r)

(p ∨ q) ↔ r

Given:p: Angles XYZ and RST are vertical angles.q: Angles XYZ and RST are congruent.Which statement is logically equivalent to p → q?

If angles XYZ and RST are congruent, then they are vertical angles.

If angles XYZ and RST are not vertical angles, then they are not congruent.

If angles XYZ and RST are not congruent, then they are not vertical angles.

If angles XYZ and RST are vertical angles, then they are not congruent.

Let p: The number is even.Let q: The number is prime.Which statement is represented by p ∧ q?

The number is even and prime.

The number is even or prime.

The number is even if the number is prime.

The number is prime if the number is even.

Which is a counterexample for the conditional statement shown?If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.

any fraction with a denominator of 0

any fraction with a numerator of 0

any fraction with a positive numerator and a negative denominator

any fraction with a negative numerator and a positive denominator

If an original conditional statement is represented using p → q, which represents the converse?

~p → ~q

~q → ~p

q → p

p → q

Read the statement.Doubling the dimensions of a rectangle increases the area by a factor of 4.If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Select two options.

p → q represents the original conditional statement.

~p → ~q represents the inverse of the original conditional statement.

q → p represents the original conditional statement.

~q → ~p represents the converse of the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

Which is a counterexample for the conditional statement shown?If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.

any fraction with a denominator of 0

any fraction with a numerator of 0

any fraction with a positive numerator and a negative denominator

any fraction with a negative numerator and a positive denominator

How can the statement be rewritten as a conditional statement in if-then form?Lines on a coordinate plane are perpendicular if they have opposite reciprocal slopes.

If lines on a coordinate plane have opposite reciprocal slopes, then they are perpendicular.

If lines are on a coordinate plane, then they are perpendicular.

If lines are on a coordinate plane, then they have opposite reciprocal slopes.

If lines have opposite reciprocal slopes and are perpendicular, then they are on a coordinate plane.

Let p: A car has automatic windows.Let q: A car has automatic seats.

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q?

the original conditional statement

the converse of the original conditional statement

the contrapositive of the original conditional statement

the inverse of the original conditional statement

Let p: x 3What is represented by p ∨ q?

x 3

x > 3 or x < −3

If x 3

x 3

How can the statement be rewritten as a conditional statement in if-then form?The sum of the digits of a two-digit number is less than the value of the original two-digit number.

If a number has two digits, then the sum of its digits is less than the value of the original two-digit number.

If a number has two digits, then the value of the original two-digit number is less than the sum of its digits.

If the sum of the digits of a two-digit number is less than the value of the original two-digit number, then the value of the original two-digit number is greater than the sum of the two digits.

If the sum of the digits of a number is less than the value of the original number, then the number is a two-digit number.

The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”What is the converse of the original statement?

If an item is not worth two quarters, then it is not worth five dimes.

If an item is worth two quarters, then it is worth five dimes.

If an item is worth five dimes, then it is worth two quarters.

If an item is not worth five quarters, then it is worth two dimes.

Which conclusion can be drawn based on the true statements shown?If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.

Based on the law of syllogism, if all the angles in a triangle are congruent, then the triangle is equilateral.

Based on the law of detachment, if all the angles in a triangle are congruent, then the triangle is equilateral.

Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.

Based on the law of detachment, if a triangle is equilateral, then all the angles are congruent.

Did you find these answers helpful?

Unit 1 TEST: Sets and Logic Answers

More from this Course

TRY EDGENUITY HACKS