Question
$\sim p (p\ v\ \sim q)\ \&\ \sim (q\ v\ \sim p)$

Answer

Truth table:
  $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
$p$ $q$ $\sim p$ $\sim q$ $p v \sim q$ $q v \sim p$ $\sim (p v \sim q)$ $\sim (q v \sim p)$ $\sim\ p\ (p\ v\ \sim q)\ \&\ \sim (q\ v\ \sim\ p)$
$1$ $T$ $T$ $F$ $F$ $T$ $T$ $F$ $F$ $F$
$2$ $T$ $F$ $F$ $T$ $T$ $F$ $F$ $T$ $F$
$3$ $F$ $T$ $T$ $F$ $F$ $T$ $T$ $F$ $F$
$4$ $F$ $F$ $T$ $T$ $T$ $T$ $F$ $F$ $F$
  $1 (\sim )$ $2(\sim )$ $1, 4(V)$ $2, 3(V)$ $5(\sim )$ $6(\sim )$ $7, 8(\&)$
Decision of the type of form for the statement: Looking at the above fact sheet, it will be seen that the representation of the given form for the statement is given in column no.$9.$ All columns in this column have an $'F'.$ This means that all substitutions for this form of statement are untrue. So it is clear that this form of statement is 'self-defeating'.

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