Maths 1 Marks Question

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.