Maths Solve the following Question.(1 Marks)

It is a true declarative sentence because a figure that has three sides is a triangle. Thus, it is a true statement.

Negation of the given statement:
All complex numbers are real numbers.

If it rains, then it is cold.

P: For every positive number x, the number (x - 1) is also positive.
P: At least for one positive real number x, the number (x - 1) is not positive.

Let q and r be the statements given by
q: x and y are odd integers.
r: x + y is an even integer.
Then, the given statement is
if q, then r,
Direct Metflod: Let q be true. Then,
q is true.
⇒ x and y are odd integers
⇒ x = 2m + 1, y = 2n + 1 for some integers m, n
⇒ x + y = (2m + 1) + (2n + 1)
⇒ x + y = (2m + 2n + 2)
⇒ x + y = 2 (m + n + 1)
⇒ x + y is an even integer
⇒ r is true.
Thus, q is true ⇒ r is true.
Hence, ''if q, then r'' is a true statement.

Consider a triangle ABC with all angles equal. Then each angle of the triangle is equal to 60".
Hence, ABC is not an obtuse angle triangle.
Therefore the following statement is false.
p: "if all the angles of a triangle are equal, then the triangle is an obtuse angled triangle".

It is an interrogative sentence, so it is not a statement.

If x is positive, then x is not less than zero.

Negation of the given statement:
There exists a policeman who is not a thief.
Or
At least one policeman is not a thief.

The statements in this pair are not the negation of each other because both statements are the same. Both the statements convey that x is an irrational number.

If Mohan is not poor, then he is not a poet.

1. I won the trophy!

It is an exclamatory sentence, so it is not a statement.

2. Please fetch me a glass of water.

It is an imperative sentence. In other words, it can be expressed either as a request or as a command. Therefore, it not a statement.

3. Can you do this work for me?

It is an interrogative sentence, so it is not a statement.

Converse:
If you feel thirsty, then it is hot outside.
Contrapositive:
If you do not feel thirsty, then it is not hot outside.

If it rains, only then the game is cancelled.

If it rains, it is not cold.

Negation of the given statement:
The earth is not round.
Or
It is not true that the earth is round

The component statements of the given compound statement are:
25 is a multiple of 5.
25 is a multiple of 8.

It is an exclamatory sentence. Therefore, it is not a statement.

The statem ant is:
"100 ism ultiple of 4 and 5"
We know that 100 is a multiple of 4 as well as 5. So, p is true statement.
Hence, the statement is true i.e. the statement "p" is a valid statement.

The component statements of the given compound statement are:
All rational numbers are real.
All real numbers are complex.

If you are not strong, then you cannot be a sailor.

Negation of the given statement:
I will go to school.

Let r and s be two statements given by
r: xy is an even integer.
s: At least one of x and y is an even integer
Lets be not true. Then,
s is not true
⇒ Both x and y are odd integers
Let x = 2n + 1 and y = 2m + 1 for some integers n and m. Then,
⇒ xy = (2n + 1)(2m + 1) for some integers n and m.
⇒ xy = 4nm + 2(n + m) + 1 for some integers n and m,
⇒ xy is an odd integer
⇒ xy is not an even integer
⇒ -r is true
Thus, -s is trua es -r is true
Hence, the given statement is true.

If you want to be happy, then you will have to be rich.

r: There exists a number x such that 0 < x < 1.
r: For every real number x, either x ≤ 0 or x < 1.

It is a true declarative sentence, so it is a statement.

Mathematics could be easy for some people, so this sentence may or may not be true. So, it is not a statement.

Exclusive OR because a lady can give a birth to a baby who is either a boy or a girl.

The tumbler is half empty if and only if the tumbler is half full.

It is a false assertive sentence, so it is a false statement.

the negation of ​the statements
a + b = b + a is true for every real number a and b.
is:
There exist real numbers a and b for which a + b ≠ b + a.
So, the given statment is of not tha negation of the first statment.

You get an A grade if and only if you do all the homework regularly.

False. Because square roots of prime num bars are irrational num bars.

The component statements of the given compound statement are:

1. All rational numbers are real.
2. All real numbers are not complex.

The compound statement is false because all real numbers are complex. The connective used is "and". So, even if one component statement is false, the compound statement is false.

Negation of the given statement:
It is not true that Ravish is honest.
Or
Ravish is not honest

Negation of the given statement:
It is not true that Bangalore is the capital of Karnataka.
Or
Bangalore is not the capital of Karnataka.

Negation of the given statement:
Both the diagonals of a rectangle do not have the same length.
Or
Both the diagonals of a rectangle have different lengths.

The component statements of the given compound statement are:

1. The sand heats up quickly in the sun.
2. Sand does not cool down fast at night.

The compound statement uses "and" as the connective. For the compound statement to be true, both the component statements must be true. The second component statement "Sand does not cool down fast at night" is false. Sand cools down fast at night. Therefore, the compound statement is false.

The argument used to check the validity of the given statement is not correct because it does not produce a contradiction.

Converse:
If you have winter clothes, then you live in Delhi.
Contrapositive:
​If you do not have winter clothes, then you do not live in Delhi.

False. Because, no radius of a circle is its chord.

The component statements of the given compound statement are:
The sky is blue.
The grass is green.

Negation of the given statement:
Some students did not complete their homework.

It is an interrogative sentence, so it is not a statement.

If it is cold, then it never rains.

If it did not snow, then Ravish does not ski.

If he tires, then he will not win.

Inclusive OR is used because a person can have both passport as well as voter registration card.