Write the solution set of the equation $x^2 + x - 2 = 0$ in roster form.

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $A \subset B$ and $B \in C,$ then $A \in C$.

Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

$(i)$ $\{1, 2, 3, 6\}$	$(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$
$(ii)$ $\{2, 3\}$	$(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$
$(iii)$ $\{M, A, T, H, E, I, C, S\}$	$(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$
$(iv)$ $\{1, 3, 5, 7, 9\}$	$(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

With reference to a universal set,the inclusion relation $(\subseteq)$ of a subset in another is:

Let $x_{1}, x_{2}, \ldots, x_{15}$ be $15$ distinct numbers chosen from $1, 2, 3, \ldots, 15$. Then,the value of $(x_{1}-1)(x_{2}-1)(x_{3}-1) \ldots (x_{15}-1)$ is

In the following,state whether $A=B$ or not:
$A=\{a, b, c, d\} ; B=\{d, c, b, a\}$