19.02 Special number sets
List all the elements of the following sets:
\left\{ \text{positive multiples of } 4 \text{ that are less than } 46 \right\}
\left\{ \text{positive even integers that are less than } 16 \right\}
\left\{ \text{positive factors of } 42 \right\}
\left\{ \text{square numbers less than } 109 \right\}
\left\{ \text{numbers that can be rolled on a standard die} \right\}
\left\{ \left. x \right\vert x \text{ is a natural number less than } 5 \right\}
\left\{ \left. x \right\vert x \text{ is an odd whole number less than } 13 \right\}
\left\{ \left. x \right\vert x \text{ is an integer between } - 8 \text{ and } - 3 \text{ (not inclusive)} \right\}
Determine whether the following statements are true or false:
3 \in \left\{ \left. x \right\vert x \text{ is a rational number} \right\}
3 \in \left\{2, 4, 5, 8\right\}
1 \in \left\{9, 8, 6, 5, 1\right\}
-0.25 \in \left\{\left. x \right\vert x \text{ is a natural number}\right\}
Consider the set A = \left\{2, 4, 6, 8\right\}. Construct a set builder notation for A.
Determine whether the following statements are true or false:
-6 \notin \Z
Determine whether the following statements are true or false:
Complete the following table to indicate whether each number belongs in the number set:
| \N | \Z | \Z^+ | \mathbf{Q} | \Reals | |
|---|---|---|---|---|---|
| 5 | Y | Y | Y | Y | Y |
| -3 | N | Y | N | N | Y |
| 123 | |||||
| -94.5 | |||||
| \dfrac{3}{4} | |||||
| \sqrt{5} | |||||
| \sqrt{-1} |
Write down the next 3 triangle numbers in this sequence:
1, 3, 6, 10, 15, ⬚, ⬚, ⬚Beginning with the eighth triangle number, write down the next 3 triangle numbers in this sequence:
36, 45, 55, 66, 78, ⬚, ⬚, ⬚
Let A = \left\{ x | \, x \text{ is a triangle number} \lt 60 \right\} and let B = \left\{ x | \, x \text{ is a positive multiple of } 3 \lt 60 \right\}.
Write all the terms in set A.
Write all the terms in set B.
Find A \cap B.
Is A \subseteq B? Explain your answer.
Is A \subseteq \N? Explain your answer.