Maths 1 Marks Question

p: Number 7 is prime.
q: Number 7 is odd.

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

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

Let p: 35 is a prime number.
q: 35 is a composite number.
Then, the negation of the given compound statement is:
~(p v q): 35 is not a prime number and it is not a composite number.

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

p: Chandigarh is Capital of Haryana.
q: Chandigarh is Capital of U.P.

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

p: A number is divisible by 2.
q: A number is divisible by 3.
p v q: A number is either divisible by 2 or 3.

If the rectangle R is rhombus, then it is square.

Here the given statement is the form p q which has the truth value T whenever either p or q or both have the truth value T. Hence, it is a true statement and its component statements are
p: 57 is divisible by 2. (False).
q: 57 is divisible by 3. (True).

p ⟷ q: A natural number is odd if and only if it is not divisible by 2.

If natural number ‘n’ is not divisible by 2 or 3, then n is not divisible by 6.

The weather will not be cold, if it does not snow.

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

Cow does not have four legs.

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

p: Chennai is in India.
q: Chennai is the Capital of Tamil Nadu.

Let p: All real numbers are rationals.
q: All real numbers are irrationals.
Then, the negation of the given compound statement is:
~(p v q): All real numbers are not rational and all real numbers are not irrational.
[~(p v q) = ~p ∧ ~ q]

Area of a circle is not same as the perimeter of the circle.

A leap year does not have 366 days.

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

q implies p ⇒ If a, b, c are in A.P then 2b = a + c.

If the triangle is not equilateral, then all three sides of the triangle are not equal.

p: 2 is factor of 12.
q: 3 is factor of 12.
r: 6 is factor of 12.
p ∧ q ∧ r: 2, 3 and 6 are factors of 12

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

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

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.

If tomorrow is Tuesday, then today is Monday.

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

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.

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

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

2 + 7 ≠ 6.

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

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

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

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

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

Violet are not blue.