225 All Questions

Give a recursive form for
1, 5, 9, 13, 17, ...

• a₁ = 1;  a_n = a_n-1 + 4
• a₁ = 1;  a_n = 2 a_n-1 - 1
• a₁ = 1;  a_n = 4n - 3

Which values should complete the truth table?

• T  F
• T  T
• F  T
• F  F

Let a_n be the n^th even number larger than 19.
What is a₃?

• 20
• 23
• 22
• 24

Identify the negation of
"John is a sophomore and he is studying French."

• John is not a sophomore, or John is not studying French.
• John is not a sophomore and he is not studying French.
• John is a freshman, and he is studying Spanish.
• John is a sophomore, or he is studying French.

True or False: The negation of 
∀ x ∈ D, P(x)
is 
∃ x ∈ D, P(x).

• True
• False

True or False: The negation of 
∃ x ∈ D, P(x)
is 
∀ x ∈ D, ¬P(x).

• True
• False

Identify the negation of 
∀ x ∈ D, P(x) → Q(x)

• ∃ x ∈ D, P(x) ∨ ¬Q(x)
• ∃ x ∈ D, ¬P(x) ∧ Q(x)
• ∀ x ∈ D, ¬(P(x) → Q(x))
• ∃ x ∈ D, P(x) ∧ ¬Q(x)

What does it mean to say that "5 divides b"?

• b = 5k for some integer k
• 5 = bk for some integer k
• 5 is a multiple of b
• b/5 is a rational number

Identify the contrapositive of
"If a is even, then 3a is a multiple of 6."

• If 3a is not a multiple of 6, then a is not even.
• If a is not even, then 3a is not a multiple of 6.
• If 3a is a multiple of 6, then a is even.
• If 6 is even a multiple, then 3!

True or False: For all n ∈ ℕ, if n is divisible by 2, then n ends in a 2.

• False
• True