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GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 10

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1 1 vote

Given the statement form below where $p, q, r, s$ are statement variables,
$$
\Biggl(\biggl(\Bigl((p \rightarrow q) \rightarrow(q \rightarrow r)\Bigl) \rightarrow(r \rightarrow s)\biggl) \vee p\Biggl) \wedge(p \rightarrow(p \rightarrow q)) \wedge p
$$
Which of the following is logically equivalent to the above?

  1. $p$
  2. $p \vee q$
  3. $p \wedge q$
  4. $p \rightarrow q$

4 Answers

0 0 votes
Use the by-case method to solve it.

Consider two cases: $\mathrm{P}=$ True , $\mathrm{P}=$ False.
0 0 votes
p → ( p → q ) is equivalent to p → q because if p is True then p → q simplifies to q.

p ∧ ( p → q) ∧ p simplifies to p ∧ q because p ∧ p is just p and p ∧ (p -> q) simplifies to p ∧ q

the expression now becomes (((p→q)→(q→r))→(r→s))∨(p∧q) = (p∧q) OR (((p→q)→(q→r))→(r→s)

so option D is correct
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