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

Answer

Truth table:
  $1$ $2$ $3$ $4$ $5$
$p$ $q$ $p \leftrightarrow q$ $\sim (p \leftrightarrow q)$ $(p \leftrightarrow  q)\ \&\ \sim (p \leftrightarrow q)$
$1$ $T$ $T$ $T$ $F$ $F$
$2$ $T$ $F$ $F$ $T$ $F$
$3$ $F$ $T$ $F$ $T$ $F$
$4$ $F$ $F$ $T$ $F$ $F$
  $1, 2( \leftrightarrow )$ $3(\sim )$ $3, 4 (\&)$
Decision of the type of form for the statement: Looking at the fact sheet above, it will be seen that the representation of the given form for the statement is in column no. $5$ is upside down. 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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