MATHS 1 Marks Question

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

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

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

p only if q ⇒ If you do not study, then you will fail.

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.

If x is nether positive nor negative then x = 0.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For every.

There exist similar triangles which are not congruent.

If xy is not positive integer, then x or y is not negative integer.

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.

If tomorrow is Tuesday, then today is Monday.

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.

q is necessary for p ⇒ If any number is prime, then its square is not prime.

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 2x = 3y then x : y = 3 : 2.

p: 0 is less than every positive integer.
q: 0 is less than every negative integer.

We know that is either true or false but not both simultaneously.
y + 9 = 7, here that the value of y is not given. So it is true for y = -2 and false for any other value of y. Hence, it is not a statement.

2 is a prime number.

p: Two line is a plane intersect at one point.
q: Two lines in a plane are parallel.

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

If he tires, then he will not win.

p ⟷ q: A triangle is an equilateral triangle if and only if all three sides of triangle are equal.

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

If Max does not study, then he will not pass the test.

You watch television if and only if your mind is free.

q if p ⇒ If take the dinner, then you will get sweet dish.

q: For every real number x, either x > 1 or x < 1.
q: At least for one real number x, neither x > 1x > 1 nor x < 1x < 1.

Negation of the given statement:
Some integers are not prime.
Or
No even integer is prime.

2 + 7 ≠ 6.

The component statements of the given compound statement are:
The earth is round.
The sun is cold.

p: Rahul passed in Hindi.
q: Rahul passed in English.
p ∧ q: Rahul passed in Hindi and English.

True. Because, for any two integers, if x - y is positive then -(x - y) is negative.

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

Negation of the given statement:
It is not true that it rained on July 4, 2005.
Or
It did not rain on July 4, 2005.

p: 100 is divisible by 3.
q: 100 is divisible by 11.
r: 100 is divisible by 5.