One
Let q represent the statement "two angles are not congruent" and let r represent the statement "not both angles are right angles". What is the symbolic representation of the following sentence? (12)
If two angles are not congruent, then both angles are right angles.
q->~r
Consider the following statements (6):
If the latch is hooked, then the door stays closed.
The latch is hooked.
Tell me the conclusion that is supported only by the Law of Detachment.
The door stays closed.
Let p represent the statement "a rectangle is a square" and let r represent the statement "all of its sides are congruent". What is the symbolic representation of the following sentence? (13)
If a rectangle is not a square, then all of its sides are congruent.
~p->r
Let s represent the statement "a quadrilateral has four edges". What symbolic statement represents the following sentence? (9)
A quadrilateral does not have four edges.
~s
Let q represent the statement "a quadrilateral is a polygon". And let s represent the statement "a square is a rectangle". What symbolic statement represents the following sentence? (10)
A quadrilateral is a polygon and a square is a rectangle.
q ^^ s
Identify the inverse of the statement below.
~q->p
q->~p
Tell me the inverse of the statement below. (2)
a -> c
~a -> ~c
Let t represent the statement "a quadrilateral is a polygon". And let s represent the statement "parallel lines intersect". What symbolic statement represents the following sentence? (11)
A quadrilateral is not a polygon or parallel lines do not intersect.
~tvv~s
A survey of 50 high school athletes showed that, to relieve pain when injured, 22 athletes use acetaminophen, 16 athletes use naproxen, and 10 athletes use both.
In the Venn Diagram below, A represents the set of athletes who use acetaminophen and N represents the set of athletes who use naproxen. Find the values of a, i, n and that represent the situation. (14)
a - 22
i - 10
n - 16
Tell me the contrapositive of the statement below. (3)
q->a
~a->~q
Choose which logic concept proves the consequence. (5)
If the latch is hooked, then the door stays closed.
If the door stays closed, then I stay outside.
Therefore, if the latch is hooked, then I stay outside.
Law of Syllogism
Jeremiah surveyed the other members of his book club. The Venn diagram below shows how many people read romance books (represented by R) and science fiction books (represented by S). Based on the diagram, how many people read romance or science fiction books? (15)
14
Rex surveyed all the students in the art department of his college on the mediums they use to paint. The Venn diagram below shows how many art students use pastels (represented by P) and oils (represented by O). Based on the diagram, how many students use pastels or oils? (17)
38
Albie surveyed all the third-year students in his college on the literature classes they are taking this semester. The Venn diagram below shows how many third-year students signed up for classic literature (represented by C) and for Spanish literature (represented by S). Based on the diagram, how many students are taking classic literature or Spanish literature? (16)
14
Choose which logic concept proves the consequence. (4)
If the latch is hooked, then the door stays closed.
The door does not stay closed.
Therefore, the latch is not hooked.
Law of Contrapositive
The following Venn Diagram shows the number of students in Darcie's Boarding School that belong to an extracurricular club. The diagram is organized by the three most popular clubs: Robotics Club, represented by R, the Fashion Design Club, represented by F, and the Spanish Club, represented by S. Based on the diagram, how many students are in the Robotics Club and in the Fashion Design Club, but not in the Spanish Club? (18)
11
Consider the following statements (7):
If Bob does buy tomatoes, then Bob makes salsa.
If Bob makes salsa, then the party is a success.
The party is not a success.
Choose the conclusion that is supported only by the Contrapositive.
Bob did not make Salsa.
Label the variations of the following statement with their types. (1)
Statement: If I catch a fish, then I will eat a fish for dinner.
1 - If I won't eat a fish for dinner, then I don't catch a fish.
2 - If I don't catch a fish, then I won't eat a fish for dinner.
3 - If I will eat a fish for dinner, then I catch a fish.
1 - Contrapositive
2 - Inverse
3 - Converse
What is the name for a line segment that connects the center of a circle to any point on the circle? (19)
Radius
What is the name for a line or line segment that splits another line segment into two congruent parts? (20)
Bisector