HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions

Using the rules in logic, write the negation of the following:

(p ∨ q) ∧ (q ∨ ∼r)

Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.

Which of the following statement is true

Negation of p → (p ˅ ∼ q) is ______

A biconditional statement is the conjunction of two ______ statements.

If p → q is an implication, then the implication ∼ q → ∼ p is called its

State the truth value of `sqrt(3)` is not an irrational number

State the truth value of (p ˅ ∼p)

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.

Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

Examine whether the statement pattern

[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.

Use quantifiers to convert the given open sentence defined on N into a true statement

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement

Y + 4 > 6

The negation of p ^ (q → r) is ______.

Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q