Chapter 5.1, Problem 13E

(a)

To determine

The list of elements of the set ${\left(R\cup S\right)}^{\prime }$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(b)

To determine

The list of elements of the set $R\cup S\cup T$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(c)

To determine

The list of elements of the set $R\cap S\cap T$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(d)

To determine

The list of elements of the set $R\cap S\cap T^{\prime }$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(e)

To determine

The list of elements of the set $R^{\prime }\cap S\cap T$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(f)

To determine

The list of elements of the set $S\cup T$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(g)

To determine

The list of elements of the set $\left(R\cup S\right)\cap \left(R\cup T\right)$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(h)

To determine

The list of elements of the set $\left(R\cap S\right)\cup \left(R\cap T\right)$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.

(i)

To determine

The list of elements of the set $\left(R^{\prime }\cap T^{\prime }\right)$ if $U=\left\{a,b,c,d,e,f\right\}$, $R=\left\{a,b,c\right\}$, $S=\left\{a,b,d\right\}$ and $T=\left\{e,f\right\}$.