Compound Statements Answers

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For which conditions is p ∨ q false?

A
p is true and q is false.
B
p is true and q is true.
C
p is false and q is true.
D
p is false and q is false.
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Let p: the book is interesting and q: the book has pictures.

Answers:
The notation p ∧ q represents the statement “The book is interesting the book has pictures.”:and
The notation p ↔ q represents the statement “The book is interesting the book has pictures.”:if and only if
The notation q ∨ p represents the statement “The book has pictures the book is interesting.”:or
The notation q → p represents the statement “The book is interesting the book has pictures.”:if
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andif✔ if and only ifor

A
and
B
if
C
✔ if and only if
D
or
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andifif and only if✔ or

A
and
B
if
C
if and only if
D
✔ or
120844

and✔ ifif and only ifor

A
and
B
✔ if
C
if and only if
D
or
120845

⇒ or

Question illustration
Answer:

120845

120847

In the Venn diagram, the blue circle represents when p is true, and the orange represents when q is true.

Answers:
A conjunction is true in region .:B
A disjunction is true in region(s) .:A, B, and C
A disjunction is false in region(s) .:D
120848

A and C✔ A, B, and CBD

A
A and C
B
✔ A, B, and C
C
B
D
D
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A and CA, B, and CB✔ D

A
A and C
B
A, B, and C
C
B
D
✔ D
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Let p: –3 > –5 and q: 3 + 2 = 5. Which statement is represented by p ∧ q?

A
–3 > –5 or 3 + 2 = 5.
B
–3 > –5 and 3 + 2 = 5.
C
If –3 > –5 then 3 + 2 = 5.
D
–3 > –5 if and only if then 3 + 2 = 5.
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Let p: it is cold, q: it is humid, and r: it is snowing. Which statement represents "It is cold and humid if and only if it is snowing”?

A
(p ∨ q) ↔ r
B
(p ↔ r) ∧ (q ↔ r)
C
[(p ∧ q) → r] ∧ [r → (p ∧ q)]
D
[(p → r) ∧ (q → r)] ∧ [(r → p) ∧ (r → q)]
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In the Venn diagram, the blue circle represents when p is true, and the orange represents when q is true.

Answers:
A conjunction is true in region .:B
A disjunction is true in region(s) .:A, B, and C
A disjunction is false in region(s) .:D

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