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

EASY

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Write the negations of following statement.

All students of this college live in the hostel.

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

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

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

p \to (~ p \lor ~ 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 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 proposition

(~ p) \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?

Write the negations of following statement. All students of this college live in the hostel.

Important Questions on Mathematical Reasoning

Learn and Prepare for any exam you want !

Write the negations of following statement.

All students of this college live in the hostel.