Chapter 11.6, Problem 16E

(a)

To determine

The description of $x\in S^{\prime }\cup T$, using logical statement forms with $p\left(x\right)$ and $q\left(x\right)$ if $p\left(x\right)$ denotes “ $x\in S$ ” and $q\left(x\right)$ denotes “ $x\in T$ ”.

(b)

To determine

The description of $x\in S\oplus T^{\prime }$, using logical statement forms with $p\left(x\right)$ and $q\left(x\right)$ if $p\left(x\right)$ denotes “ $x\in S$ ” and $q\left(x\right)$ denotes “ $x\in T$ ”.

(c)

To determine

The description of $x\in S^{\prime }\cap T^{\prime }$, using logical statement forms with $p\left(x\right)$ and $q\left(x\right)$ if $p\left(x\right)$ denotes “ $x\in S$ ” and $q\left(x\right)$ denotes “ $x\in T$ ”.

(d)

To determine

The description of $x\in {\left(S\cup T\right)}^{\prime }$, using logical statement forms with $p\left(x\right)$ and $q\left(x\right)$ if $p\left(x\right)$ denotes “ $x\in S$ ” and $q\left(x\right)$ denotes “ $x\in T$ ”.