On the power set P(X), the symmetric difference A △ B = (A ∖ B) ∪ (B ∖ A) has identity:

A △ ∅ = A, so ∅ is the identity.

Daily Math Problems — June 26, 2026: Calculus, Systems of Linear Equations, Algebra

Problems & worked solutions

RO M1

The limit $\lim_{n \to \infty} 2^{n}$ equals:

Show answer & worked solution

$2^{n}$ grows without bound: $\lim 2^{n} = \infty$ .

RO M1

The solution of ${\begin{cases} x + y + z = 6 \\ x - y = 0 \\ y + z = 5 \end{cases}$ is:

Show answer & worked solution

$x = y$ . Then $2 y + z = 6$ and $y + z = 5$ , so $y = 1$ and $z = 4$ . Solution: $(1, 1, 4)$ .

RO M1

On the power set $P (X)$ , the symmetric difference $A △ B = (A ∖ B) \cup (B ∖ A)$ has identity:

Show answer & worked solution

$A △ \emptyset = A$ , so $\emptyset$ is the identity.

Problems & worked solutions

RO M1

The limit $\lim_{n \to \infty} 2^{n}$ equals:

Show answer & worked solution

$2^{n}$ grows without bound: $\lim 2^{n} = \infty$ .

RO M1

The solution of ${\begin{cases} x + y + z = 6 \\ x - y = 0 \\ y + z = 5 \end{cases}$ is:

Show answer & worked solution

$x = y$ . Then $2 y + z = 6$ and $y + z = 5$ , so $y = 1$ and $z = 4$ . Solution: $(1, 1, 4)$ .

RO M1

On the power set $P (X)$ , the symmetric difference $A △ B = (A ∖ B) \cup (B ∖ A)$ has identity:

Show answer & worked solution

$A △ \emptyset = A$ , so $\emptyset$ is the identity.