HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write the negation of the following.

If it is raining then we will go and play football.

Write the negation of the following.

All-natural numbers are whole numbers.

Write the negation of the following.

∀ n ∈ N, n² + n + 2 is divisible by 4.

Write the negation of the following.

∃ x ∈ N such that x – 17 < 20

Using the rule of negation write the negation of the following with justification.

∼ q → p

Using the rule of negation write the negation of the following with justification.

p ∧ ∼ q

Using the rule of negation write the negation of the following with justification.

p ∨ ∼ q

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) ∧ r

Using the rule of negation write the negation of the following with justification.

p → (p ∨ ∼ q)

Using the rule of negation write the negation of the following with justification.

∼ (p ∧ q) ∨ (p ∨ ∼ q)

Using the rule of negation write the negation of the following with justification.

(p ∨ ∼ q) → (p ∧ ∼ q)

Using the rule of negation write the negation of the following with justification.

(∼ p ∨ ∼ q) ∨ (p ∧ ∼ q)

Select and write the correct answer from the given alternative of the following question:

The negation of inverse of ∼p → q is ________.

The negation of p ∧ (q → r) is ________.

Write the negation of the following:

∀ n ∈ A, n + 7 > 6.

Write the negation of the following:

∃ x ∈ A, such that x + 9 ≤ 15.

Write the negation of the following:

Some triangles are equilateral triangle.

Find the distance of the point `4hat"i" - 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" - 6hat"k")` = 21.

Find the distance of the point (1, 1 –1) from the plane 3x +4y – 12z + 20 = 0.

Solve the following:

Find the distance of the point `3hat"i" + 3hat"j" + hat"k"` from the plane `bar"r".(2hat"i" + 3hat"j" + 6hat"k")` = 21.