1.3.5 Quiz - Week Three: Inductive & Deductive Reasoning

Find the next item in the pattern. 0.03, 0.06, 0.09, 0.12,...

0.15

Find the next item in the pattern. 3, 5, 7, 9, 11,...

13

Write the definition as a biconditional statement. An equilateral triangle is a triangle with three congruent sides.

A triangle is equilateral if and only if it has three congruent sides.

Write the converse, inverse, and contrapositive of the conditional statement. Find the truth value of each. If John is on vacation, then he is in London.

Converse: If John is in London, then he is on vacation. Inverse: If John is not on vacation, then he is not in London. Contrapositive: If John is not in London, he is not on vacation.

Identify the converse and a biconditional statement for the conditional. If an angle is a straight angle, then its measure is 180°.

converse: If an angle measures 180°, then the angle is a straight angle. biconditional: An angle is a straight angle if and only if its measure is 180°.

Dyann takes a bus to work every day. On Monday the trip took 34 minutes. On Tuesday the trip took 36 minutes. On Wednesday the trip took 35 minutes. On Thursday the trip took 34 minutes. Dyann determines that the trip to work on Friday will take about 35 minutes. Does her conclusion use inductive, or deductive reasoning?

inductive reasoning

Determine if the following conjecture is valid. Given: If m is an even number, then m is an integer. If m is an integer, then m is a rational number. 18.113 is a rational number. Conclusion: 18.113 is an even number.

not valid

Determine whether the following conjecture is valid. Given: An American citizen who is at least 16 years old is eligible to get a driver's license. Julian is a 25-year-old American citizen. Conclusion: Julian is eligible to get a driver's license.

valid

Write the definition as a biconditional statement. A triangle which has no congruent sides is a scalene triangle.

A triangle is scalene if and only if it has no sides that are congruent.

Write the converse, inverse, and contrapositive of the conditional statement. Find the truth value of each. If Julie scores 90 or above, then she receives an A.

Converse: If Julie receives an A, then her score is 90 or above. Inverse: If Julie does not score 90 or above, then she will not get an A. Contrapositive: If Julie does not get an A, then her score is not 90 or above.

Identify the hypothesis and conclusion of the conditional. A quadrilateral with congruent angles and sides is called a square.

H: A quadrilateral has congruent angles and sides. C: The quadrilateral is a square.

Identify the hypothesis and conclusion of the conditional. In a right triangle, (hypotenuse)2 = (adjacent side)2 + (opposite side)2.

H: A triangle is a right triangle. C: (hypotenuse)2 = (adjacent side)2 + (opposite side)2

Convert the following statement into a conditional. A quadrilateral with 4 congruent sides and 4 congruent angles is a square.

If a quadrilateral has 4 congruent sides and 4 congruent angles, then it is a square.

Which Law deals with the truth value of p and q?

Law of Detachment

If p → q and q → r and r → s, then p → s. This is most similar to which Law?

Law of Syllogism

Identify the converse and a biconditional statement for the conditional. If two lines are parallel, then they are equidistant everywhere.

converse: If two lines are equidistant everywhere, then they are parallel lines. biconditional: Two lines are parallel if and only if they are equidistant everywhere.

Identify the converse and a biconditional statement for the conditional. If two lines intersect, then they are not parallel.

converse: If two lines are not parallel, then they intersect. biconditional: Two lines intersect if and only if they are not parallel.

At Kennedy High School, students must take History before they take Geography. Peter is in Geography, so he must have taken History. Does the conclusion use inductive or deductive reasoning?

deductive reasoning

The doctor has advised Catherine to take aspirin only after meals. Catherine is taking aspirin, so she must have just eaten. Does the conclusion use inductive or deductive reasoning?

deductive reasoning

Determine if the following conjecture is true. If not, give a counterexample. The square of an even integer is odd.

false; 122 = 144

Determine if the statement is true. If false, give a counter example. If a2 = 225, then a = 15.

false; a = −15

Determine if the biconditional is true. If false, give a counterexample. An angle is a right angle if and only if it is not obtuse.

false; m∠1 = 70°, ∠1 is not a right angle

Determine if this conjecture is true. If not, give a counterexample. Two complementary angles are not congruent.

false; m∠1 = m∠2 = 45°

Determine whether the biconditional statement is true or false. If false, give a counterexample. x − y is positive if and only if |x| > y.

false; x = −1, y = 0

Determine if this conjecture is true. If not, give a counterexample. The difference of two negative numbers is a negative number.

false; −11 − (−13) = 2

Determine whether the following conjecture is valid. Given: If x is an odd number, then x is an integer. If x is an integer, then x is a rational number. 3 is an odd number. Conclusion: 3 is a rational number.

valid