Question

Let the set U = {1, 2, 3, 4, 5}, be the universe. Let Y = {(n+2)| n = 2, 3} 5 and X = {3, 4}. Write the following sets using set builder notation

Answer 1

Set builder notation is a mathematical notation of describing a set by listing its elements or demonstrating its properties that its members must satisfy. Set $U$ we can write in the form: $U=\{u: (u\in{\mathbb{N}})\land(1\leq u\leq 5)\}$. $Y$ can be rewritten in the following form: $Y=\{n:(n\in{\mathbb{N}})\land((n=4)\lor(n=5))\}$. X can be rewritten in the following form: $X=\{x:(x\in{\mathbb{N}})\land((x=3)\lor(x=4))\}$. In case we assume that $U$ is the universe and we consider only subsets of $U$, we get: $Y=\{n\in U: (n=4)\lor(n=5)\}$ and $X=\{x\in U: (x=3)\lor(x=4)\}$.