MATHS 1 Marks Question

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

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

The statement is:
r: 60 ism ultiple of 3 or 5
is a com pound statement of the following statements:
p: 60 is multiple of 3
q: 60 is multiple of 5
Suppose q is false. That is, 60 is not a multiple of 5. Clearly p is true.
Thus, if we assume that q is false, then p is true.
Hence, the statement is true i.e. the statement "r" is a valid statement.

It is a false assertive sentence. Two non-empty sets with no common elements can have an empty intersection. Therefore, it is a statement.

Negation of the given statement:
Some birds do not sing.
Or
There exists a bird that does not sing.

Exclusive OR is used because students can opt for either Hindi or Sanskrit as their third language.

If the triangle is equilateral, then all three angles of the triangle are equal.

Violet are not blue.

It is a declarative sentence, which may be true or false but cannot be both at the same time, so it is a statement.

p is sufficient for q ⇒ If an integer is divisible by 5, then its unit digits are 0 or 5.

Without knowing the sentence, we cannot decide whether it is true or false. So, it is not a statement.

It is not true that every rhombus is a square because some rhombi may have all angles other than 90. So, it is a false statement.

If the opposite angles of a quadrilateral are supplementary, then S is cyclic.

True. Because a circle is an ellipse that has equal axes.

We cannot decide whether this sentence is true or false without knowing the value of x. So, it is not a statement.

If she does not earn money, then she will not work.

If you must visit Taj Mahal, then you go to Agra.

If p, then q ⇒ If the number is odd, then its square is odd number.

Let p: 6 is divisible by 2.
q: 6 is divisible by 3.
Then, the negation of the given compound statement is:
~(p ∧ q): 6 is not divisible by 2 or it is not divisible by 3

Let p: All prime integers are even.
q: All prime integers are odd.
Then, the negation of the given compound statement is given by ~ (p v q):
All prime integers are not even and all prime integers are not odd.

If it rains, then there is a traffic jam.

It is necessary to have a passport to log on to the server.

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

If you pay a subscription fee, then you can access the website.

Negation of the given statement:
There exists a number which is not equal to its square.

Inclusive OR because a person could have both ration card as well as passport.

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

Every real number is not an irrational number.

Negation of everyone is not everyone. So, negation of the given statement should be “Not everyone in India speaks Hindi”, “Someone in India does not speaks Hindi”, “At least one person in India who does not speaks Hindi”. “No person in India speaks Hindi” cannot be the negation of the given statement as this means no one speaks Hindi which does not means not everyone.

p: A rectangle is a quadrilateral.
q: A rectangle is a 5-sides polygon.

p: Plants use sunlight for photosynthesis.
q: Plants use water for photosynthesis.
r: Plants use carbon-dioxide for photosynthesis.

The number 17 is not prime.

p: x is an odd integer.
q: (x + 1) is an odd integer.
p v q: Either x or (x + 1) is an odd integer.

If it rains, then it is cold.

p: Students can take Hindi as an optional paper.
q: Students can take English as an optional paper.
p v q: Students can take Hindi or English as an optional paper.

The component statements of the given compound statement are:

1. To enter into a public library, children need an identity card from the school.
2. To enter into a public library, children need a letter from the school authorities.

The compound statement is true because both component statements are true.

A quadrilateral is a rectangle if and only if it is equiangular.

Let p:|x| is equal to x.
q:|x| is equal to -x.
Then, the negation of the given compound statement is:
~(p v q): |x| is not equal to JC and it is not equal to -x.

If the triangle is right triangle, then the sum of the squares of two sides of a triangle is equal to the square of third side.

Let p: All rational numbers are real.
q: All rational numbers are complex.
~p: All rational numbers are not real.
~q; All rational numbers are not complex.
Then, the negation of the given compound statement is:
~(p ∧ q): All rational numbers are not real or not complex.
[~(p ∧ q) = ~p v ~ q]

If they do not drive the car, then there is no snow.

If n is not an integer, then it is not a natural number.

The statement is:
"125 is multiple of 5 and 7"
Since 125 is a multiple of 5 but it is not a multiple of 7. So, q is not a true statement i.e. the statement "q" is not a valid statement.

If x 2 > 1 then x is not a real number such that 0 < x < 1.

Negation of the given statement:
The sun is not cold.
Or
It is not true that the sun is cold.

False. Because, a chord does not have to pass through the centre.

If the ratio of corresponding sides of two triangles are equal, then triangles are similar.

The given statement in this pair are the negation of each other.