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

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?

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

(p ∨ q) ∧ (q ∨ ∼r)

Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.

Which of the following statement is true

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

State the truth value of `sqrt(3)` is not an irrational number