Register

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

• edited by
608 views
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
Voting & Accepting an answer helps improve the community
Answer:
← Previous · GO Classes DA Test S...Next → · GO Classes DA Test S...
← Previous in category · GO Classes DA Test S...Next in category → · GO Classes DA Test S...
Position:
Show:

Related questions

2 2 votes
1 1 answer
589
589 views
GO Classes asked Jan 10, 2025
589 views
GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 6
Consider the following interpretation of a language with a unary predicates $P, Q$, and a binary predicate $R$.Universe $=\{1,2,3,4\}$$P=\{\langle 1\rangle,\langle 3\rang...
2 2 votes
1 1 answer
373
373 views
GO Classes asked Jan 10, 2025
373 views
GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 7
Suppose the marked diagram below conveys information about relationships between pirates, ruffians and scoundrels. We use shading to indicate that a region contains no el...
1 1 vote
1 1 answer
344
344 views
GO Classes asked Jan 10, 2025
344 views
GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 8
The statement form $(p \Leftrightarrow r) \Rightarrow(q \Leftrightarrow r)$ is equivalent to$[(\sim p \vee r) \wedge(p \vee \sim r)] \vee \sim[(\sim q \vee r) \wedge(q \v...
0 0 votes
1 1 answer
341
341 views
GO Classes asked Jan 10, 2025
341 views
GO Classes DA Test Series | Artificial Intelligence | Propositional and Predicate logic | Question: 9
Which of the following formulas is a formalization of the sentence:"Every connected and circuit-free graph is a tree"Where $\operatorname{cir}(\mathrm{x})$ means " x has ...