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

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Write the following compound statement symbolically.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.

Write converse, inverse and contrapositive of the following statement.

If x < y then x² < y² (x, y ∈ R)

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 ______.