Let S be a non-empty subset of R . Consider the following statement : P : There is a rational number x ∈ S such that x > 0 . Which of the following statements is the negation of the statement P ?

Every rational number x ∈ S satisfies x ≤ 0 .

There is a rational number x ∈ S such that x < 0 .

There is no rational number x ∈ S such that x ≤ 0 .

x ∈ S and x ≤ 0 x is not rational.

Let S be a non-empty subset of R . Consider the following statement : P : There is a rational number x ∈ S such that x > 0 . Which of the following statements is the negation of the statement P ?

Every rational number x ∈ S satisfies x ≤ 0 .

The negation of “ ∀ n ∈ N , n + 7 > 6 ” is ….

∃ n ∈ N , such that n + 7 ≤ 6

∃ n ∈ N , such that n + 7 ≥ 6

∃ n ∈ N , such that n + 7 < 6

Negation of the statement: 5 is an integer or 5 is irrational is:

5 is not an integer and 5 is not irrational

5 is not an integer 5 is not irrational

5 is irrational or 5 is an integer

5 is an integer and 5 irrational

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Let $S$ be a non-empty subset of $R$ . Consider the following statement : $P$ : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement $P$ ?

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Important Questions on Mathematical Reasoning

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

p \to (p \land ~ q)

is false, then the truth values of

p

and

q

are respectively

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The negation of

“ \forall n \in N, n + 7 > 6 ”

is ….

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

Negation of the statement:

\sqrt{5}

is an integer or

5

is irrational is:

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The statement

(p \to (q \to p)) \to (p \to (p \lor q))

is :

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

p \to (~ p \lor ~ q)

is false, then the truth values of

p

and

q

are, respectively

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

Let

p, q, r

be three statements such that the truth value of

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

F

. Then the truth values of

p, q, r

are respectively :

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

For two statements

p

and

q

, the logical statement

(p \to q) \land (q \to ~ p)

is equivalent to

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The negation of the statement "For all real numbers

x

and

y, x + y = y + x

" is

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

For any two statement

p

and

q,

the negative of the expression

p \lor (~ p \land q)

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The negation of the Boolean expression

~ s \lor (~ r \land s)

is equivalent to

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The proposition

p \to ~ (p \land ~ q)

is equivalent to :

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The proposition

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

is equivalent to

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The Boolean expression

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

is equivalent to

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The negation of the statement “All continuous functions are differentiable”

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

p : 4

is an even prime number,

q : 6

is a divisor of

12

and

r :

the

HCF

4

and

6

2

, then which of the following is correct?

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The statement

A \to (B \to A)

is equivalent to :

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The negation of the statement ''

72

is divisible by

2

and

3

'' is

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The Boolean expression

\sim (p \Rightarrow (\sim q))

is equivalent to

EASY

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

The Boolean expression

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

is equivalent to

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Mathematical Reasoning>New Statements from Old

Consider the following three statements:

$P : 5$ is a prime number

$Q : 7$ is a factor of $192$

$R : LCM$ of $5$ and $7$ is $35$

Then the truth value of which one of the following statements is true?

Let S be a non-empty subset of R. Consider the following statement : P: There is a rational number x∈S such that x>0. Which of the following statements is the negation of the statement P ?

Important Questions on Mathematical Reasoning

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Let $S$ be a non-empty subset of $R$ . Consider the following statement : $P$ : There is a rational number $x \in S$ such that $x > 0$ . Which of the following statements is the negation of the statement $P$ ?