Answer
See step by step work for solution.
Work Step by Step
a)
p$\quad$q$\quad$r$\quad$$\neg{q}$$\quad$$\neg{q}$ $ \vee$ r$\quad$p $\rightarrow $ ( $\neg{q}$ $ \vee$ r )
T$\quad$T$\quad$T $\quad$F$\quad$ $\quad$T$\quad$$\quad$$\quad$T
T$\quad$T$\quad$F $\quad$F$\quad$ $\quad$F$\quad$$\quad$$\quad$F
T$\quad$F$\quad$T $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
T$\quad$F$\quad$F $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
F$\quad$T$\quad$T $\quad$F$\quad$ $\quad$T$\quad$$\quad$$\quad$T
F$\quad$T$\quad$F $\quad$F$\quad$ $\quad$F$\quad$$\quad$$\quad$T
F$\quad$F$\quad$T $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
F$\quad$F$\quad$F $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
b)
p$\quad$q$\quad$r$\quad$$\neg{p}$$\quad$q$\rightarrow$r$\quad$$\neg{p}$$\rightarrow$(q$\rightarrow$r)
T$\quad$T$\quad$T $\quad$F$\quad$ $\quad$T$\quad$$\quad$$\quad$T
T$\quad$T$\quad$F $\quad$F$\quad$ $\quad$F$\quad$$\quad$$\quad$T
T$\quad$F$\quad$T $\quad$F$\quad$ $\quad$T$\quad$$\quad$$\quad$T
T$\quad$F$\quad$F $\quad$F$\quad$ $\quad$F$\quad$$\quad$$\quad$T
F$\quad$T$\quad$T $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
F$\quad$T$\quad$F $\quad$T$\quad$ $\quad$F$\quad$$\quad$$\quad$F
F$\quad$F$\quad$T $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
F$\quad$F$\quad$F $\quad$T$\quad$ $\quad$T$\quad$$\quad$$\quad$T
c)
p$\quad$q$\quad$r$\quad$p$\rightarrow$q$\quad$$\neg{p}$$\quad$$\neg{p}$$\rightarrow$r$\quad$(p$\rightarrow$q)$\vee$($\neg{p}
$$\rightarrow$r)
T$\quad$T$\quad$T$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$T$\quad$F$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$F$\quad$T$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$F$\quad$F$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$T$\quad$T$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$T$\quad$F$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$ T
F$\quad$F$\quad$T$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$F$\quad$F$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$ T
d)
p$\quad$q$\quad$r$\quad$p$\rightarrow$q$\quad$$\neg{p}$$\quad$$\neg{p}$$\rightarrow$r$\quad$(p$\rightarrow$q)$\wedge$($\neg{p}$ $\rightarrow$r)
T$\quad$T$\quad$T$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$T$\quad$F$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$F$\quad$T$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ F
T$\quad$F$\quad$F$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ F
F$\quad$T$\quad$T$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$T$\quad$F$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$ F
F$\quad$F$\quad$T$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$F$\quad$F$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad $ F
e)
p$\quad$q$\quad$r$\quad$p$\leftrightarrow$q$\quad$$\neg{q}$$\quad$$\neg{q}$$\leftrightarrow$r$\quad$(p$\leftrightarrow$q)$\wedge$($\neg{q}$ $\leftrightarrow$r)
T$\quad$T$\quad$T$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$F$\quad$$\quad$$\quad$ T
T$\quad$T$\quad$F$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$F$\quad$T$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
T$\quad$F$\quad$F$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$ F
F$\quad$T$\quad$T$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$F$\quad$$\quad$$\quad$ F
F$\quad$T$\quad$F$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$F$\quad$T$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$ T
F$\quad$F$\quad$F$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$ T
f)
p$\quad$q$\quad$r$\quad$$\neg{p}$$\quad$$\neg{q}$$\quad$$\neg{p}$$\leftrightarrow$$\neg{q}$$\quad$ q$\leftrightarrow$r$\quad$$\quad$($\neg{p}$$\leftrightarrow$$\neg{q}$)$\wedge$(q $\leftrightarrow$r)
T$\quad$T$\quad$T$\quad$F$\quad$$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$$\quad$T
T$\quad$T$\quad$F$\quad$F$\quad$$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$$\quad$F
T$\quad$F$\quad$T$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$$\quad$T
T$\quad$F$\quad$F$\quad$F$\quad$$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$$\quad$F
F$\quad$T$\quad$T$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$$\quad$F
F$\quad$T$\quad$F$\quad$T$\quad$$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$$\quad$T
F$\quad$F$\quad$T$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$F$\quad$$\quad$$\quad$$\quad$F
F$\quad$F$\quad$F$\quad$T$\quad$$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$T$\quad$$\quad$$\quad$$\quad$T
