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DM G+1 Exam 2026-2027 BANK QUESTIONS WITH
DETAILED VERIFIED ANSWERS EXAM QUESTIONS
WILL COME FROM HERE (100% Latest Already Graded
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QUESTION 1
In propositional logic, which of the following statements is a tautology?
A) P AND NOT P
B) P OR NOT P
C) P IMPLIES NOT P
D) P AND Q
Answer: B
Explanation: A tautology is a compound proposition that is always true
regardless of the truth values of its components. P OR NOT P is the law
of excluded middle, which holds for any proposition P. If P is true, the
statement is true because P is true. If P is false, NOT P is true, making
the disjunction true. Option A is a contradiction, always false. Option C
is not always true; it is true only when P is false. Option D is true only
when both P and Q are true.
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QUESTION 2
The converse of the implication P IMPLIES Q is:
A) Q IMPLIES P
B) NOT P IMPLIES NOT Q
C) NOT Q IMPLIES NOT P
D) P IMPLIES NOT Q
Answer: A
Explanation: The converse of an implication P IMPLIES Q is formed by
swapping the hypothesis and conclusion, resulting in Q IMPLIES P.
Option B is the inverse, option C is the contrapositive, and option D is a
different implication altogether. In logical reasoning, the converse is not
logically equivalent to the original implication.
QUESTION 3
Which logical equivalence is represented by NOT (P AND Q) = NOT P OR
NOT Q?
A) Commutative law
B) Associative law
C) De Morgan's law
D) Distributive law
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Answer: C
Explanation: De Morgan's laws provide relationships between
conjunctions and disjunctions under negation. Specifically, NOT (P AND
Q) is equivalent to NOT P OR NOT Q. Similarly, NOT (P OR Q) is
equivalent to NOT P AND NOT Q. These laws are fundamental in
simplifying logical expressions and are named after Augustus De
Morgan, a British mathematician.
QUESTION 4
In predicate logic, the universal quantifier is denoted by:
A) EXISTS
B) FOR ALL
C) NOT
D) AND
Answer: B
Explanation: The universal quantifier, denoted by the symbol FOR ALL,
expresses that a property holds for all elements in a domain. It is used in
statements like FOR ALL x, P(x), meaning P(x) is true for every x in the
domain. The existential quantifier EXISTS asserts that there exists at
least one element for which P(x) is true. NOT and AND are logical
connectives, not quantifiers.
QUESTION 5
Which of the following is a valid argument form?
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A) Modus ponens
B) Modus tollens
C) Hypothetical syllogism
D) All of the above
Answer: D
Explanation: Modus ponens, modus tollens, and hypothetical syllogism
are all valid forms of deductive reasoning. Modus ponens: P IMPLIES Q,
P, therefore Q. Modus tollens: P IMPLIES Q, NOT Q, therefore NOT P.
Hypothetical syllogism: P IMPLIES Q, Q IMPLIES R, therefore P IMPLIES
R. Each of these argument forms preserves truth, meaning that if the
premises are true, the conclusion must be true.
QUESTION 6
What is the truth value of P AND Q when P is false and Q is true?
A) True
B) False
C) Undefined
D) Cannot be determined
Answer: B
Explanation: In classical logic, the conjunction P AND Q is true only
when both P and Q are true. Since P is false, the conjunction is false
regardless of Q's truth value. This demonstrates the principle that a
DM G+1 Exam 2026-2027 BANK QUESTIONS WITH
DETAILED VERIFIED ANSWERS EXAM QUESTIONS
WILL COME FROM HERE (100% Latest Already Graded
A+
QUESTION 1
In propositional logic, which of the following statements is a tautology?
A) P AND NOT P
B) P OR NOT P
C) P IMPLIES NOT P
D) P AND Q
Answer: B
Explanation: A tautology is a compound proposition that is always true
regardless of the truth values of its components. P OR NOT P is the law
of excluded middle, which holds for any proposition P. If P is true, the
statement is true because P is true. If P is false, NOT P is true, making
the disjunction true. Option A is a contradiction, always false. Option C
is not always true; it is true only when P is false. Option D is true only
when both P and Q are true.
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QUESTION 2
The converse of the implication P IMPLIES Q is:
A) Q IMPLIES P
B) NOT P IMPLIES NOT Q
C) NOT Q IMPLIES NOT P
D) P IMPLIES NOT Q
Answer: A
Explanation: The converse of an implication P IMPLIES Q is formed by
swapping the hypothesis and conclusion, resulting in Q IMPLIES P.
Option B is the inverse, option C is the contrapositive, and option D is a
different implication altogether. In logical reasoning, the converse is not
logically equivalent to the original implication.
QUESTION 3
Which logical equivalence is represented by NOT (P AND Q) = NOT P OR
NOT Q?
A) Commutative law
B) Associative law
C) De Morgan's law
D) Distributive law
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Answer: C
Explanation: De Morgan's laws provide relationships between
conjunctions and disjunctions under negation. Specifically, NOT (P AND
Q) is equivalent to NOT P OR NOT Q. Similarly, NOT (P OR Q) is
equivalent to NOT P AND NOT Q. These laws are fundamental in
simplifying logical expressions and are named after Augustus De
Morgan, a British mathematician.
QUESTION 4
In predicate logic, the universal quantifier is denoted by:
A) EXISTS
B) FOR ALL
C) NOT
D) AND
Answer: B
Explanation: The universal quantifier, denoted by the symbol FOR ALL,
expresses that a property holds for all elements in a domain. It is used in
statements like FOR ALL x, P(x), meaning P(x) is true for every x in the
domain. The existential quantifier EXISTS asserts that there exists at
least one element for which P(x) is true. NOT and AND are logical
connectives, not quantifiers.
QUESTION 5
Which of the following is a valid argument form?
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A) Modus ponens
B) Modus tollens
C) Hypothetical syllogism
D) All of the above
Answer: D
Explanation: Modus ponens, modus tollens, and hypothetical syllogism
are all valid forms of deductive reasoning. Modus ponens: P IMPLIES Q,
P, therefore Q. Modus tollens: P IMPLIES Q, NOT Q, therefore NOT P.
Hypothetical syllogism: P IMPLIES Q, Q IMPLIES R, therefore P IMPLIES
R. Each of these argument forms preserves truth, meaning that if the
premises are true, the conclusion must be true.
QUESTION 6
What is the truth value of P AND Q when P is false and Q is true?
A) True
B) False
C) Undefined
D) Cannot be determined
Answer: B
Explanation: In classical logic, the conjunction P AND Q is true only
when both P and Q are true. Since P is false, the conjunction is false
regardless of Q's truth value. This demonstrates the principle that a
