HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Important Questions

Write converse, inverse and contrapositive of the following statement. "If voltage increases then current decreases".

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

p → (p ∨ ∼ q)

Construct the switching circuit of the following:

(∼ p ∧ q) ∨ (p ∧ ∼ r)

Give an alternative equivalent simple circuit for the following circuit:

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

(p ∨ q) ∧ (q ∨ ∼r)

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

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

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 ______.

Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q

Simplify the given circuit by writing its logical expression. Also, write your conclusion.

Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p