Section 1
Sets, Statements, and Reasoning
Which sentences are statements? If a sentence is a statement, classify it as true or false.a) Where do you live?b) $4+7 \neq 5$c) Washington was the first U.S. president.d) $x+3=7$ when $x=5$
Which sentences are statements? If a sentence is a statement, classify it as true or false.a) Chicago is located in the state of Illinois.b) Get out of here!c) $x<6$ (read as " $x$ is less than 6 ") when $x=10$d) Babe Ruth is remembered as a great football player.
Give the negation of each statement.a) Christopher Columbus crossed the Atlantic Ocean.b) All jokes are funny.
Give the negation of each statement.a) No one likes me.b) Angle 1 is a right angle.
Classify each statement as simple, conditional, a conjunction, or a disjunction.If Alice plays, the volleyball team will win.
Classify each statement as simple, conditional, a conjunction, or a disjunction.Alice played and the team won.
Classify each statement as simple, conditional, a conjunction, or a disjunction.The first-place trophy is beautiful.
Classify each statement as simple, conditional, a conjunction, or a disjunction.An integer is odd or it is even.
Classify each statement as simple, conditional, a conjunction, or a disjunction.Matthew is playing shortstop.
Classify each statement as simple, conditional, a conjunction, or a disjunction.You will be in trouble if you don't change your ways.
State the hypothesis and the conclusion of each statement.If you go to the game, then you will have a great time.
State the hypothesis and the conclusion of each statement.If two chords of a circle have equal lengths, then the arcs of the chords are congruent.
State the hypothesis and the conclusion of each statement.If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
State the hypothesis and the conclusion of each statement.If $\frac{a}{b}=\frac{c}{d},$ where $b \neq 0$ and $d \neq 0,$ then $a \cdot d=b \cdot c$
State the hypothesis and the conclusion of each statement.Corresponding angles are congruent if two parallel lines are cut by a transversal.
Corresponding angles are congruent if two parallel lines are cut by a transversal.Vertical angles are congruent when two lines intersect.
State the hypothesis and the conclusion of each statement.All squares are rectangles.
State the hypothesis and the conclusion of each statement.Base angles of an isosceles triangle are congruent.
Classify each statement as true or false.If a number is divisible by $6,$ then it is divisible by 3
Classify each statement as true or false.Rain is wet and snow is cold.
Classify each statement as true or false.Rain is wet or snow is cold.
Classify each statement as true or false.If Jim lives in Idaho, then he lives in Boise.
Classify each statement as true or false.Triangles are round or circles are square.
Classify each statement as true or false.Triangles are square or circles are round.
Name the type of reasoning (if any) used.While participating in an Easter egg hunt, Sarah notices that each of the seven eggs she has found is numbered. Sarah concludes that all eggs used for the hunt are numbered.
Name the type of reasoning (if any) used.You walk into your geometry class, look at the teacher, and conclude that you will have a quiz today.
Name the type of reasoning (if any) used.Albert knows the rule "If a number is added to each side of an equation, then the new equation has the same solution set as the given equation." Given the equation $x-5=7$ Albert concludes that $x=12$
Name the type of reasoning (if any) used.You believe that "Anyone who plays major league baseball is a talented athlete." Knowing that Duane Gibson has just been called up to the major leagues, you conclude that Duane Gibson is a talented athlete.
Name the type of reasoning (if any) used.As a handcuffed man is brought into the police station, you glance at him and say to your friend, "That fellow looks guilty to me."
Name the type of reasoning (if any) used.While judging a science fair project, Mr. Cange finds that each of the first 5 projects is outstanding and concludes that all 10 will be outstanding.
Name the type of reasoning (if any) used.You know the rule "If a person lives in the Santa Rosa Junior College district, then he or she will receive a tuition break at Santa Rosa." Emma tells you that she has received a tuition break. You conclude that she resides in the Santa Rosa Junior College district.
Name the type of reasoning (if any) used.As Mrs. Gibson enters the doctor's waiting room, she concludes that it will be a long wait.
Use intuition to state a conclusion.You are told that the opposite angles formed when two lines cross are vertical angles. In the figure, angles 1 and 2 are vertical angles. Conclusion?(Figure can't copy)
Use intuition to state a conclusion.In the figure, point $M$ is called the midpoint of line segment AB. Conclusion?(Figure can't copy)
Use intuition to state a conclusion.The two triangles shown are similar to each other. Conclusion?(Figure can't copy)
Use intuition to state a conclusion.Observe (but do not measure) the following angles. Conclusion?(Figure can't copy)
Use induction to state a conclusion.Several movies directed by Lawrence Garrison have won Academy Awards, and many others have received nominations. His latest work, $A$ Prisoner of Society, is to be released next week. Conclusion?
Use induction to state a conclusion.On Monday, Matt says to you, "Andy hit his little sister at school today." On Tuesday, Matt informs you, "Andy threw his math book into the wastebasket during class." On Wednesday, Matt tells you, "Because Andy was throwing peas in the school cafeteria, he was sent to the principal's office." Conclusion?
Use induction to state a conclusion.While searching for a classroom, Tom stopped at an instructor's office to ask directions. On the office bookshelves are books titled Intermediate Algebra, Calculus, Modern Geometry, Linear Algebra, and Differential Equations. Conclusion?
Use induction to state a conclusion.At a friend's house, you see several food items, including apples, pears, grapes, oranges, and bananas. Conclusion?
Use deduction to state a conclusion, if possible.If the sum of the measures of two angles is $90^{\circ},$ then these angles are called "complementary." Angle 1 measures 27" and angle 2 measures $63^{\circ} .$ Conclusion?
Use deduction to state a conclusion, if possible.If a person attends college, then he or she will be a success in life. Kathy Jones attends Dade County Community College. Conclusion?
Use deduction to state a conclusion, if possible.All mathematics teachers have a strange sense of humor. Alex is a mathematics teacher. Conclusion?
Use deduction to state a conclusion, if possible.All mathematics teachers have a strange sense of humor. Alex has a strange sense of humor. Conclusion?
Use deduction to state a conclusion, if possible.If Stewart Powers is elected president, then every family will have an automobile. Every family has an automobile. Conclusion?
Use deduction to state a conclusion, if possible.If Tabby is meowing, then she is hungry. Tabby is hungry. Conclusion?
Use deduction to state a conclusion, if possible.If a person is involved in politics, then that person will be in the public eye. June Jesse has been elected to the Missouri state senate. Conclusion?
Use deduction to state a conclusion, if possible.If a student is enrolled in a literature course, then he or she will work very hard. Bram Spiegel digs ditches by hand six days a week. Conclusion?
Use deduction to state a conclusion, if possible.If a person is rich and famous, then he or she is happy. Marilyn is wealthy and well known. Conclusion?
Use deduction to state a conclusion, if possible.If you study hard and hire a tutor, then you will make an A in this course. You make an A in this course. Conclusion?
Use Venn Diagrams to determine whether the argument is valid or not valid.1) If an animal is a cat, then it makes a "meow" sound.2) Tipper is a cat.C) Then Tipper makes a "meow" sound.
Use Venn Diagrams to determine whether the argument is valid or not valid.1) If an animal is a cat, then it makes a "meow" sound.2) Tipper makes a "meow" sound.C) Then Tipper is a cat.
Use Venn Diagrams to determine whether the argument is valid or not valid.1) All Boy Scouts serve the United States of America.2) Sean serves the United States of America.C) Sean is a Boy Scout.
Use Venn Diagrams to determine whether the argument is valid or not valid.1) All Boy Scouts serve the United States of America.2) Sean is a Boy Scout.C) Sean serves the United States of America.
Where $A=\{1,2,3\}$ and $B=\{2,4,6,8\},$ classify each of the following as true or false.a) $A \cap B=\{2\}$b) $A \cup B=\{1,2,3,4,6,8\}$c) $A \subseteq B$
P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false.a) $\quad(P \text { and } Q)$ or $R$b) $\quad(P \text { or } Q)$ and $R$
P is a true statement, while Q and R are false statements. Classify each of the following statements as true or false.a) $(P \text { and } Q)$ or $\sim R$b) $(P \text { or } Q)$ and $\sim R$