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

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls

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

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`

Write the dual of the following statements: (p ∨ q) ∧ T

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

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.

Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n² + n is an even number and n² - n is an odd number.

Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.

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

If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p

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:

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 

Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]