HSC Commerce: Marketing and Salesmanship 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

Write the dual of the following statements:

Madhuri has curly hair and brown eyes.

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. 

Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 

Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )

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

If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )

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

(a) p ∧ (q → r)

(b)  ~P ∨ ~q

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)]

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. 

Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 

Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10

Use the quantifiers to convert the following open sentence defined on N into true statement:
x² ≥ 1

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 negation of the Following Statement :
∀ y ∈  N, y² + 3 ≤ 7

Write the negation of the following statement : 
If the lines are parallel then their slopes are equal.