Name: _________________________________ Date: _____________ 2.1 – 2.4 Study Guide

Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the

next item in the sequence.

1) 1, 10, 100, 1000, …. 2) 1, 65 ,

75 ,

85 , …

3) The product of two odd numbers 4) the difference of two even numbers

5) The sum of an odd and even number 6) the quotient of two even numbers

7) 8) 12, 6, 3, 1.5, 0.75, …

9) Each spring, Rachel starts sneezing when the pear trees on her street blossom. She reasons that she is allergic to pear trees. Find a counter example to Rachel’s conjecture.

10) If S, T, and U are collinear and ST = TU, then T is the midpoint of line SU.

11) Point S is between R and T.

Use the following statements to write a compound statement for each conjunction. Then find its truth

value. Remember a conjunction is TRUE only when __________ statements are ____________.

p: The figure is a triangle. q: The figure has two congruent sides r: The figure has three acute angles

1) p and q 2) 𝑞 ⋀~𝑟 3) not p and not r

Name: _________________________________ Date: _____________ 2.1 – 2.4 Study Guide

Use the following statements to write a compound statement for each disjunction. Then find its truth

value. Remember a disjunction is FALSE only when ___________ statements are ____________.

p: January is a fall month. q: January has only 30 days. r: January 1 is the first day of a new year.

1) p or r 2) 𝑝⋁𝑞 3) 𝑞 ⋁~𝑟

Construct truth tables for each.

1) 𝑝⋀𝑟 2) ~𝑞⋁~𝑟 3) 𝑝⋁𝑟

The Venn diagram shows the results of a pet store survey to determine the pets customers owned.

a) How many people own a dog and cat?

b) How many people own a dog or fish?

c) How many people own a dog, cat and fish?

d) How many people own a dog, cat or fish?

e) What does the 2 in the middle of the Venn diagram represent?

f) What does the 25 outside the region mean?

g) How many people own just a fish?

Name: _________________________________ Date: _____________ 2.1 – 2.4 Study Guide

h) What does the 10 in the Venn diagram represent?

Identify the hypothesis and conclusion of each conditional statement.

1) If today is Wednesday, then tomorrow is Thursday.

2) If 4x – 5 = 15, then x = 5.

Write each statement in if-then form.

1) Collinear points lie on the same line.

2) “Those who do not remember the past are condemned to repeat it.” (George Santayana)

Determine the truth value of each conditional statement.

1) If a and b are negative, then a + b is also negative.

2) If you have five dollars, then you have five one-dollar bills.

Write the converse, inverse, and contrapositive of the following true statement.

1) If 89 is divisible by 2, then 89 is an even number.

2) If two angles are complementary, then the sum of their measures is 90.

Name: _________________________________ Date: _____________ 2.1 – 2.4 Study Guide

Determine whether each conclusion is based on inductive or deductive reasoning.

1) A dental assistant notices a patient has never been on time for an appointment. She concludes the patient will be late for her next appointment.

2) If Eduardo decides to go to a concert tonight, he will miss football practice. Tonight, Eduardo went to a concert. Eduardo missed football practice.

Use the Law of Syllogism to draw a valid conclusion from each set of statements, if possible.

1) If Tina has a grade point average of 3.0 or greater, she will be on the honor roll. If Tina is on the honor roll, then she will have her name in the school paper.

2) (1) If you interview for a job, then you wear a suit. (2) If you interview for a job, then you will update your resume. A. If you wear a suit, then you will update your resume. B. If you update your resume, then you will wear a suit. C. If you do not interview for a job, then you will not wear a suit. D. No valid conclusion

Determine whether the stated conclusion is valid based on the given information. Then state whether

your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If not, write invalid

and explain your reasoning.

1) Given: If you study for the test, then you will receive a high grade. Conclusion: Your grade on the test is high.

2) Given: If a number is divisible by 6, then the number is divisible by 3. Conclusion: 18 is divisible by 3

3) Given: If an angle is supplementary to an obtuse angle, then it is acute. If an angle is acute, then its measure is less than 90. Conclusion: ?