HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Important Questions

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)

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

Draw a Venn diagram for the truth of the following statement : 

All rational number are real numbers. 

Draw Venn diagram for the truth of the following statements : 

Some rectangles are squares. 

Express the truth of each of the following statements using Venn diagrams: 

(a) No circles are polygons

(b) Some quadratic equations have equal roots 

Evaluate: ∫ x . log x dx

Using the rules of negation, write the negatlon of the following: 

(a) p ∧ (q → r)

(b)  ~P ∨ ~q

Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .

Write the Truth Value of the Negation of the Following Statement :

The Sun sets in the East. 

Using the Venn diagram, examine the logical equivalence of the following statements: 

(a) Some politicians are actors.

(b) There are politicians who are actors.

(c) There are politicians who are not actors.

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

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

Consider the following statements.

1. If D is dog, then D is very good.
2. If D is very good, then D is dog.
3. If D is not very good, then D is not a dog.
4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.

Choose the correct alternative:

Negation of p → (p ˅ ~q) is