Compound Statements Answers

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The coordinate plane is separated into four quadrants as shown.

Question illustration
A
quadrant 1 because both x and y are positive coordinates
B
quadrant 3 because both x and y are negative coordinates
C
quadrants 1, 2, and 4 because in these quadrants x, y, or both are positive coordinates
D
quadrants 2, 3, and 4 because in these quadrants x, y, or both are negative coordinates
3

Which disjunction is always true for any real number x?

A
A number, x, is less than 0 or greater than 1.
B
A number, x, is less than 0 or greater than 0.
C
A number, x, is greater than 5 or less than 10.
D
A number, x, is greater than 5 or less than 1.
5

Which conjunction about whole numbers is true?

A
The sum of two non-zero even numbers is even and less than the addends.
B
The sum of two non-zero even numbers is even and greater than the addends.
C
The difference of two non-zero even numbers is odd and less than the larger number.
D
The difference of two non-zero even numbers is odd and greater than the larger number.
6

The diagram represents responses to a survey that include statements p and q.

Question illustration
A
The number of responses for which p ∧ q is 20.
B
The number of responses for which p ∨ q is 26.
C
The number of responses for which p ∧ q is 46.
D
The number of responses for which p ∨ q is 66.
7

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

A
x 3
B
x > 3 or x < −3
C
If x 3
D
x 3
8

Let p: The kitchen is clean.Let q: The bedroom is clean.Which statement is true if the kitchen is clean but the bedroom is not clean?

A
If p is true, then q is true.
B
Statement q is true if and only if p is true.
C
Both p and q are true.
D
Statement p or q is true.
9

Let p: A number is greater than 25.Let q: A number is less than 35.If p ∧ q is true, then what could the number be? Select two options.

A
24
B
28
C
32
D
36
E
40
11

Which statements are true for rows A and E? Select two options.

A
p ↔ q
B
q ↔ p
C
q ↔ r
D
r ↔ p
E
r ↔ q
12

The diagram represents two statements: p and q.

Question illustration
A
p ∨ q
B
p → q
C
q ∧ p
D
q → p
13

The diagram represents two statements: p and q.

Question illustration
A
p ∨ q
B
p → q
C
q ∧ p
D
q → p
14

The diagram represents responses to a survey that include statements p and q.

Question illustration
A
The number of responses for which p ∧ q is 20.
B
The number of responses for which p ∨ q is 26.
C
The number of responses for which p ∧ q is 46.
D
The number of responses for which p ∨ q is 66.
15

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

Question illustration
A
40
B
54
C
66
D
80
16

The truth table represents statements p, q, and r. pqrp ∧ qp ∧ r AT T T T T BT T F T F CT F T F T DT F F F F EF T T F F FF T F F F GF F T F F HF F F F F

A
A and B
B
A, B, and C
C
B and E
D
B, C, and E
17

Let p: A number is greater than 25.Let q: A number is less than 35.If p ∧ q is true, then what could the number be? Select two options.

A
24
B
28
C
32
D
36
E
40
18

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

A
x 3
B
x > 3 or x < −3
C
If x 3
D
x 3
19

Which disjunction is always true for any real number x?

A
A number, x, is less than 0 or greater than 1.
B
A number, x, is less than 0 or greater than 0.
C
A number, x, is greater than 5 or less than 10.
D
A number, x, is greater than 5 or less than 1.
20

Which conjunction about whole numbers is true?

A
The sum of two non-zero even numbers is even and less than the addends.
B
The sum of two non-zero even numbers is even and greater than the addends.
C
The difference of two non-zero even numbers is odd and less than the larger number.
D
The difference of two non-zero even numbers is odd and greater than the larger number.

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