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

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)]

Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.

Write the following compound statement symbolically.

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

Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → r)

Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

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:

Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .

If p ∧ q is F, p → q is F then the truth values of p and q are ________.

If A = {1, 2, 3, 4, 5} then which of the following is not true?