turkey-yks 2015 Q13

turkey-yks · Other · lys1-math Probability Definitions Combinatorial Counting (Non-Probability)
Let $\mathbf { A } = \{ \mathbf { a } , \mathbf { b } , \mathbf { c } , \mathbf { d } \}$. For non-empty subsets $X , Y$ of A
$$\begin{aligned} & X \cap Y = \emptyset \\ & X \cup Y = A \end{aligned}$$
How many ordered pairs (X, Y) are there such that these conditions hold?
A) 6
B) 8
C) 10
D) 12
E) 14
Let $\mathbf { A } = \{ \mathbf { a } , \mathbf { b } , \mathbf { c } , \mathbf { d } \}$. For non-empty subsets $X , Y$ of A

$$\begin{aligned}
& X \cap Y = \emptyset \\
& X \cup Y = A
\end{aligned}$$

How many ordered pairs (X, Y) are there such that these conditions hold?\\
A) 6\\
B) 8\\
C) 10\\
D) 12\\
E) 14