Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.8 Junior Find the answer

Given the sets $M=\{0,1,2\}$ and $N=\{y|y=\sin \frac {π}{2}x,x\in M\}$ , determine the intersection $M\cap N=(\quad\quad)$ .

Pick one

Solution

First, we find the set $N$ . Since $x\in M=\{0,1,2\}$ , substitute each value of $x$ into the function $y=\sin \frac {π}{2}x$ .
- When $x=0$ , $y=\sin \frac {π}{2}\cdot 0=0$ .
- When $x=1$ , $y=\sin \frac {π}{2}\cdot 1=1$ .
- When $x=2$ , $y=\sin \frac {π}{2}\cdot 2=0$ .

Thus, set $N=\{0,1\}$ .

Next, we find the intersection $M\cap N$ . By definition, the intersection of two sets contains only the elements common to both sets. In this case, $M\cap N=\{0,1\}$ .

Therefore, the correct answer is: $\boxed{\text{C: }\{0,1\}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.