Compound Statements Answers

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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
2
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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
3

Which biconditional statement is true?

A
A shape is a rectangle if and only if the shape has exactly four sides and four right angles.
B
A shape is a trapezoid if and only if the shape has a pair of parallel sides.
C
A shape is a triangle if and only if the shape has three sides and three acute angles.
D
A shape is a square if and only if the shape has exactly four congruent sides.
4

The diagram represents three statements about animals at the zoo: p, q, and r.

Question illustration
A
15
B
17
C
20
D
22
5

Let p: x = 4Let q: y = −2Which represents "If x = 4, then y = −2”?

A
p ∨ q
B
p ∧ q
C
p → q
D
p ↔ q
6

Let p ↔ q represent the statement "He is wearing a coat if and only if the temperature is below 30°F.”Which represents p ∧ q?

A
He is wearing a coat or the temperature is below 30°F.
B
He is wearing a coat and the temperature is below 30°F.
C
If he is wearing a coat, then the temperature is below 30°F.
D
If he is not wearing a coat, then the temperature is not below 30°F.
7

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
8

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

Question illustration
A
40
B
54
C
66
D
80
9

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.
10

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

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