Question

Let A, B, and C be sets. Show that$(A-B)-C$ is not necessarily equal to$A-(B-C)$

Short answer

Let $A=\left\{1\right\},B=\varnothing ,C=\left\{1\right\}$.

Then $(A-B)-C=\varnothing$, but$A-(B-C)=1$

Step-by-step solution

Step: 1

Let $A=\left\{1\right\},B=\varnothing ,C=\left\{1\right\}$

Then $(A-B)-C=\varnothing$, but $A-(B-C)=1$