Intro to Algebra Week 1

True or False?

0 ∈ ℕ

• True

• False

True or False?

If f: A → B is a surjective function, then f(A) = B

• True

• False

True or False?

If f: A → B is a function such that for all a ∈ A, f(a) ∈ B, then f is surjective.

• True

• False

True or False?

If f: A → B is a function such that for all b ∈ B, we can find a ∈ A such that f(a) = b, then f is surjective.

• True

• False

True or False?

If f: A → B is a function and there exists a, a' ∈ A such that f(a) ≠ f(a'), then f is injective.

• True

• False

True or False?

f: A → B is a function. If for every a, a' ∈ A with a ≠ a', f(a) ≠ f(a'), then f is injective.

• True

• False

True or False?

ℤ × ℤ = ℤ

• True

• False

True or False?

Addition is not commutative

• True

• False

True or False?

Subtraction is not commutative

• True

• False

True or False?

Matrix multiplication is commutative.

• True

• False