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

Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)

Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p

Construct the switching circuit for the statement (p ∧ q) ∨ (~ p) ∨ (p ∧ ~ q).

If A = {2, 3, 4, 5, 6}, then which of the following is not true?

(A) ∃ x ∈ A such that x + 3 = 8

(B) ∃ x ∈ A such that x + 2 < 5

(C) ∃ x ∈ A such that x + 2 < 9

(D) ∀ x ∈ A such that x + 6 ≥ 9

Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p

Construct the new switching circuit for the following circuit with only one switch by simplifying the given circuit:

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.