Daily Math · 2026-06-24

Question 1

A monoid is a semigroup that also has:

Accepted Answer

A monoid = semigroup + identity element. (A group adds the inverse-element axiom.)

Answer

inverses for every element

Answer

an identity element

Answer

commutativity

Answer

a zero element

Question 2

$(\mathbb{Z}, +, \cdot)$ has zero divisors?

Accepted Answer

In $\mathbb{Z}$, the product of two non-zero integers is non-zero — so $\mathbb{Z}$ has no zero divisors. It's an integral domain.

Answer

yes, $2 \cdot 0 = 0$

Answer

no, $\mathbb{Z}$ is an integral domain

Answer

only on negative integers

Answer

only multiples of $6$

Question 3

If the data set $\{x_1, \ldots, x_n\}$ has standard deviation $\sigma$, the standard deviation of $\{2x_1, \ldots, 2x_n\}$ is:

Accepted Answer

$\sigma(c \cdot x) = |c| \sigma(x)$. With $c = 2$: $\sigma(2x) = 2\sigma$.

Answer

$\sigma$

Answer

$\sigma + 2$

Answer

$2\sigma$

Answer

$4\sigma$

Problems & worked solutions