HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Important Questions

State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.

State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.

Write the truth value of the negation of the following statement : 

cos² θ + sin² θ = 1, for all θ ∈ R 

Express the truth of each of the following statements using Venn diagram.
(1) All teachers are scholars and scholars are teachers.
(2) If a quadrilateral is a rhombus then it is a parallelogram..

Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."

Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.

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.