Let A= : = and B= : =1 be two sets.

Question

Let $A=\{	heta : \sin	heta=	an	heta\}$ and $B=\{	heta : \cos	heta=1\}$ be two sets. Then:

Accepted Answer

$$A: \sin\theta=\frac{\sin\theta}{\cos\theta} \implies \sin\theta(\cos\theta-1)=0 \implies \theta = 0,\pi,2\pi,3\pi,\dots$$

$$B: \cos\theta=1 \implies \theta=0,2\pi,4\pi,\dots$$

Every element of $B$ is in $A$, but $A$ contains extra elements (like $\pi$) not in $B$. So $B\subseteq A$, i.e. $B\subset A$.

Solutions · 1