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.

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

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

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.

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

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

Every real number is not an irrational number.

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.

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.

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

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

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

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

p: x is even integers.
q: y is even integers.
p ∧ q: x andy are even integers.

If x ≠ 3, then x ≠ y or y ≠ 3.

Let p: A triangle has 3-sides.
q: A triangle has 4-sides.
Then, the negation of the given compound statement is:
~(p v q): A triangle has neither 3-sides nor 4-sides.

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

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

p ⟷ q: The unit digit of on integer is zero, if and only if it is divisible by 5.