Write the following sets in roster form :

$D = \{ x:x$ is a prime number which is divisor of $60\} $

$D = \{ x:x$ is a prime number which is divisor of $60\} $

$2$ | $60$ |

$2$ | $30$ |

$3$ | $15$ |

$5$ |

$\therefore 60=2 \times 2 \times 3 \times 5$

The elements of this set are $2,3$ and $5$ only.

Therefore, this set can be written in roster form as $D=\{2,3,5\}$

What universal set $(s)$ would you propose for each of the following :

The set of isosceles triangles

Write the following intervals in set-builder form :

$\left( { - 3,0} \right)$

Write the following intervals in set-builder form :

$\left[ { - 23,5} \right)$

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If $A \subset B$ and $x \notin B,$ then $x \notin A$

Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$