GATE
DPP 01
Data Science & Artificial Intelligence
Artificial Intelligence
Adversarial
Q1 What is the truth table for the propositional
(B) ¬P ∧ Q
connective "→"?
(C) Q → ¬P
(A) P | Q | P→Q --------- T | T | T T | F | F F | T | T
(D) ¬Q → P
F|F|T
Q5 What is the biconditional of the propositions "P"
(B) P | Q | P→Q --------- T | T | F T | F | T F | T | F
F|F|T
and "Q"?
(A) P ↔ Q
(B) P ∧ Q
(C) P | Q | P→Q --------- T | T | T T | F | F F | T | T
F|F|T
(D) P | Q | P→Q --------- T | T | F T | F | F F | T | T
F|F|T
(C) ¬P ∨ ¬Q
(D) ¬P ∧ ¬Q
Q6 What is a tautology?
(A) A proposition that is always true
(B) A proposition that is always false
Q2 What is the negation of the proposition "P ∧ Q"?
(A) ¬P ∨ ¬Q
(C) A proposition that is sometimes true and
sometimes false
(D) A proposition that is neither true nor false
(B) ¬(P ∧ Q)
(C) ¬P ∧ ¬Q
Q7 What is a contradiction?
(D) (¬P) ∧ (¬Q)
(A) A proposition that is always true
Q3 What is the disjunction of the propositions "P"
and "¬Q"?
(B) A proposition that is always false
(C) A proposition that is sometimes true and
sometimes false
(A) P ∨ ¬Q
(D) A proposition that is neither true nor false
(B) P ∧ ¬Q
(C) ¬P ∨ ¬Q
Q8 Which of the following propositional formulas is
(D) ¬P ∧ ¬Q
a tautology?
Q4 What is the conditional of the propositions "¬P"
and "Q"?
(A) (P → Q) ∧ ¬Q
(B) (P ∨ Q) → (¬P → Q)
(C) (¬P ∧¬Q) → ¬(P ∨ Q)
(A) ¬P → Q
(D) ¬(P → Q) → Q
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Answer Key
Q1
(A)
Q5
(A)
Q2
(B)
Q6
(A)
Q3
(A)
Q7
(B)
Q4
(A)
Q8
(B)
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Hints & Solutions
Q1 Text Solution:
Q5 Text Solution:
The propositional connective "→" is called
The biconditional of two propositions is true if
implication. It is true if and only if the
and only if both propositions have the same
antecedent (P) is false or the consequent (Q) is
truth value (i.e., both are true or both are false).
true.
The biconditional of "P" and "Q" is "P ↔ Q".
Q2 Text Solution:
Q6 Text Solution:
The negation of a proposition is the opposite of
A tautology is a compound proposition that is
the proposition. The negation of "P ∧ Q" is "¬(P ∧
always true, regardless of the truth values of its
Q)".
components.
Q3 Text Solution:
Q7 Text Solution:
The disjunction of two propositions is true if at
A contradiction is a compound proposition that
least one of the propositions is true. The
is always false, regardless of the truth values of
disjunction of "P" and "¬Q" is "P ∨ ¬Q".
its components.
Q4 Text Solution:
Q8 Text Solution:
The conditional of two propositions is true if the
Propositional formulas are evaluated using truth
antecedent (¬P) is false or the consequent (Q) is
tables. The only propositional formula in the
true. The conditional of "¬P" and "Q" is "¬P → Q".
choices that is always true is (P ∨ Q) → (¬P → Q)
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