HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).

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

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)

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

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

(p ∨ q) ∧ (q ∨ ∼r)

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q → p

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

~ p → (p → ~ q)

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 ______.

Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.

Write the negation of the following statement.

∃ n ∈ N, (n² + 2) is odd number.

Write the negation of the following statement.

Some continuous functions are differentiable.

Write the converse, inverse, and contrapositive of the following statement.

If he studies, then he will go to college.

Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)

Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]

Using the truth table, prove the following logical equivalence.

p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)