Question
(p & ~ q) & (p $\rightarrow$ q)

Answer

Truth table:
  1 2 3 4 5 6
p q ~ q p & ~ q p $\rightarrow$ q (p & ~ q) & (p $\rightarrow$ q)
1 T T F F T F
2 T F T T F F
3 F T F F T F
4 F F T F T F
  2 (~) 1, 3 (&) 1, 2($\rightarrow$) 4, 5(&)
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. Done in 6. All rows in this column have the same ‘T’. 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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