Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 2 - Subjective Problem 2

Considet the set A= $\{1, 2,\dots, n\} =[n]$ , find the number of k-tuples $(A_1,A_2,\dots, A_k)$ , where $A_i\subseteq A$ and $k, n$ are positive integers, such that
{a.} $A_1\cap A_2 \cap \ldots \cap A_k=\Phi$ .
{b.} $A_1\subseteq A_2\subseteq \ldots \subseteq A_k$ .

This problem is a part of Tessellate S.T.E.M.S (2019)

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$