The negation of the Boolean expression x ↔ ~ y is equivalent to:

( x ∧ y ) ∨ ( ~ x ∧ ~ y )

( ~ x ∧ y ) ∨ ( ~ x ∧ ~ y )

( x ∧ ~ y ) ∨ ( ~ x ∧ y )

( x ∧ y ) ∧ ( ~ x ∨ ~ y )

Given the following two statements: S 1 : q ∨ p → p ↔ ~ q is a tautology S 2 : ~ q ∧ ~ p ↔ q is a fallacy. Then :

both S 1 and S 2 are not correct.

EASY

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$(p \to q) \leftrightarrow (q \lor ~ p)$ is

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Important Questions on Mathematical Reasoning

EASY

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is

HARD

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The logical statement

[~ (~ p \lor q) \lor (p \land r)] \land (~ q \land r)

is equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Consider the following two statements:

P

: If

7

is an odd number, then

7

is divisible by

2

Q

: If

7

is a prime number, then

7

is an odd number.

If

V_{1}

is the truth value of the contrapositive of

P

and

V_{2}

is the truth value of contrapositive of

Q

, then the ordered pair

(V_{1}, V_{2})

equals

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which one of the following is a tautology?

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The expression

~ (~ p \to q)

is logically equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which one of the following Boolean expression is a tautology?

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The Boolean Expression

(p \land \sim q) \lor q \lor (\sim p \land q)

is equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The negation of the Boolean expression

x \leftrightarrow ~ y

is equivalent to:

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The statement pattern

(∽ p \land q)

is logically equivalent to

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which of the following statement pattern is a tautology?

EASY

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which of the following statements is a tautology?

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The Boolean expression

((p \land q) \lor (p \lor ~ q)) \land (~ p \land ~ q)

is equivalent to

EASY

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which of the following sentences is/are statement

(s)

(i)

10

is less than

5

(ii)

All rational numbers are real numbers.

(iii)

Today is a sunny day.

EASY

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which one of the following statements is not a tautology?

HARD

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which of the following is a tautology?

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Which of the following is not equivalent to

~ p \land q

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

Given the following two statements:

$(S_{1}) : (q \lor p) \to (p \leftrightarrow ~ q)$ is a tautology
$(S_{2}) : ~ q \land (~ p \leftrightarrow q)$ is a fallacy. Then :

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The contrapositive of the statement 'If two numbers are not equal, then their squares are not equal', is

MEDIUM

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The statement

(p \to q) \to [(~ p \to q) \to q]

HARD

Mathematics>Algebra>Mathematical Reasoning>Validity of a Statement

The negation of

∽ s \lor (∽ r \land s)

is equivalent to

p→q↔q∨~p is

Important Questions on Mathematical Reasoning

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$(p \to q) \leftrightarrow (q \lor ~ p)$ is