In propositional logic, which of the following formulas is not a valid tautology?
P∨¬P
P∧¬P
(P→Q)∨(¬P∨Q)
P→(P∨Q)
Correct Answer
Option 2
Solution
In propositional logic, a tautology is a formula that is true in every possible truth assignment.
So option B is not valid one.
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
Which of the following statements is not a property of Breadth-First Search (BFS)?
BFS always finds the shortest path in an unweighted graph.
BFS explores all nodes at the present depth before moving to nodes at the next depth level.
BFS has an exponential time complexity in the worst case.
BFS is guaranteed to work optimally for weighted graphs with arbitrary edge costs.
Correct Answer
Option 4
Solution
For weighted graphs with arbitrary edge costs,we use Dijkstra’s algorithm
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
In an informed search algorithm like A, when is a heuristic considered admissible?*
When it overestimates the true cost to reach the goal.
When it is always consistent, following the triangle inequality.
When it underestimates or equals the true cost to reach the goal.
When it guarantees optimality by ignoring some paths.
Correct Answer
Option 3
Solution
A heuristic is admissible if it never overestimates the actual cost to reach the goal. This ensures that A* will find the optimal solution because it will not be misled by an overestimate of the remaining cost.
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
In adversarial search, what is the primary goal of using the evaluation function in games like chess or checkers?
To determine the next move by evaluating every possible move's full game outcome.
To estimate the likelihood of a draw in the game.
To approximate the value of a game position when the search tree cannot be fully explored.
To minimize the time required to reach a solution by ignoring suboptimal moves.
Correct Answer
Option 3
Solution
In games like chess or checkers, the evaluation function estimates the value of a position when it’s impossible to search all the way to the game’s end (due to time constraints or complexity).
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
In adversarial search, which of the following statements is correct regarding the Minimax algorithm?
Minimax only works when both players have full information.
Minimax assumes that both players will play optimally.
Minimax will always return the same result as Alpha-Beta Pruning.
Minimax is guaranteed to win for the maximizer in all games.
Correct Answer
Option 2
Solution
Minimax assumes that both players are playing optimally: the maximizer tries to maximize their score, and the minimizer tries to minimize the score.
Difficulty Level: 1
Positive Marks: 1.00
Negative Marks: 0.33
In a search problem, which heuristic function would ensure that A behaves exactly like Uniform-Cost Search?
A heuristic function that overestimates the cost to reach the goal.
A heuristic function that is always zero.
A heuristic function that always underestimates the cost.
A heuristic function that is non-admissible.
Correct Answer
Option 2
Solution
If the heuristic function h(n)h(n)h(n) is always zero, A* will effectively reduce to Uniform-Cost Search, as it will only rely on the actual cost to reach a node, ignoring any estimate of the cost to reach the goal.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Which of the following statements about informed and uninformed search is true?
Uninformed search algorithms can always find the shortest path faster than informed search algorithms.
Informed search algorithms guarantee finding the shortest path if a heuristic function is admissible and consistent.
Both informed and uninformed searches require heuristic information to guarantee completeness.
Breadth-First Search is an example of an informed search algorithm.
Correct Answer
Option 2
Solution
Informed search algorithms guarantee finding the shortest path if a heuristic function is admissible and consistent.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by?
~P V ~Q
P ∧ ~Q
P V Q
P ∧ Q
Correct Answer
Option 2
Solution
The second part of the statement is negated, hence negation operator is used.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘We should be honest or dedicated but not overconfident.’ is best represented by?
~P V ~Q V R
P ∧ ~Q ∧ R
P V Q ∧ R
P V Q ∧ ~R
Correct Answer
Option 4
Solution
The third part of the statement is negated, hence negation operator is used, for (‘or’ –V) is used and for(’but’- ∧).
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational”
Correct Answer
Option 3
Solution
(A) "There exist some numbers which are either real OR rational"
(B) "All real numbers are rational"
(C) "There exist some numbers which are both real AND rational"
(D) "There exist some numbers for which rational implies real"
Clearly answer C is correct among all
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be a predicate which denotes that x is connected. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”?
Correct Answer
Option 4
Solution
Option A and option C are same G(x)-->C(x) can also be written as ~G(x) or C(x), and they are the correct representation. Option C says :There exists a graph and graph is not connected ,which is equivalent to given sentence. Option D: Every x which is graph is not connected. Option D is correct choice
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
The CORRECT formula for the sentence, “not all rainy days are cold” is
Correct Answer
Option 4
Solution
Note that (p ∧ ~q) ≡ ~(p -> q). So it means rainy day to cold implication is false for some days. Which means not all rainy days are cold.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Which one of the first order predicate calculus statements given below correctly express the following
English statement?
Tigers and lions attack if they are hungry or threatened.
Correct Answer
Option 4
Solution
The statement "Tigers and lions attack if they are hungry or threatened" means that if an animal is either tiger or lion, then if it is hungry or threatened, it will attack. So option (D) is correct.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
Let P, Q and R be three atomic prepositional assertions. Let X denote (P v Q) → R and Y denote (P → R) v (Q → R). Which one of the following is a tautology?
X → Y
Y → X
¬ Y → X
Correct Answer
Option 2
Solution
X = (P ⋁ Q) → R
= ~(P ⋁ Q) ⋁ R
= (~P ⋀ ~Q) ⋁ R
= (~P ⋁ R) ⋀ (~Q ⋁ R)
= (P → R) ⋀ (Q → R)
X → Y is true as (A ⋀ B) → (A ⋁ B) is always TRUE
but reverse implication is not always true.
Difficulty Level: 1
Positive Marks: 2.00
Negative Marks: 0.66
The following propositional statement is
(P → (Q v R)) → ((P ^ Q) → R)
satisfiable but not valid
valid
a contradiction
none of the above
Correct Answer
Option 1
Solution
The correct option is A Satisfiable but not valid
(P→(Q∨R))→((P∧Q)→R
≡(P→Q+R)→(PQ→R)
≡[P′+Q+R]→[(PQ)′+R]
≡[P′+Q+R]→[P′+Q′+R]
≡(P′+Q+R)′+P′+Q′+R
≡PQ′R′+P′+Q′+R
≡Q′+Q′PR′+P′+R
≡Q′+P′+R (by absorption law)
Which is a contingency (i.e. satisfiable but not valid).
