#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## Solutions for Chapter 1: Mathematical Logic

Below listed, you can find solutions for Chapter 1 of Maharashtra State Board SCERT Maharashtra Question Bank for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board.

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board Chapter 1 Mathematical Logic MCQ

#### 2 Marks

Which of the following statement is true

3 + 7 = 4 or 3 – 7 = 4

If Pune is in Maharashtra, then Hyderabad is in Kerala

It is false that 12 is not divisible by 3

The square of any odd integer is even

**Choose the correct alternative :**

Which of the following is not a statement?

Smoking is injuries to health

2 + 2 = 4

2 is the only even prime number.

Come here

If p is any statement then ( p ˅ ∼ p) is a

Contingency

Contradiction

Tautology

None of these

**Choose the correct alternative :**

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is

Contradiction

Tautology

Neither (i) not (ii)

None of the these

Negation of p → (p ˅ ∼ q) is

∼ p → (∼ p ˅ q)

p ˄ (∼ p ˄ q)

∼ p ˅ (∼ p ˅ ∼ q)

∼ 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

∼ p ∨ ∼ p

∼ (p ∧ q)

∼ (p ∨ q)

p ∨ ∼ q

A biconditional statement is the conjunction of two ______ statements

Negative

Compound

Connective

Conditional

If p → q is an implication, then the implication ∼ q → ∼ p is called its

Converse

Contrapositive

Inverse

Alternative

The negation of the statement (p ˄ q) → (r ˅ ∼ p)

p ˄ q ˄ ∼ r

(p ˄ q) ˅ r

p ˅ q ˅ ∼ r

(p v q) ˄ (r ˅ s)

**Choose the correct alternative:**

The false statement in the following is ______.

p ˄ (∼ p) is contradiction

(p → q) ↔ (∼ q → ∼ p) is a contradiction

∼ (∼ p) ↔ p is a tautology

p ˅ (∼ p) ↔ p is a tautology

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board Chapter 1 Mathematical Logic Very Short Answers

#### 1 mark

Find the negation of 10 + 20 = 30

State the truth Value of x^{2} = 25

Write the negation of p → q

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

State the truth value of (p ˅ ∼p)

State the truth value of (p ˄ ∼p)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board Chapter 1 Mathematical Logic Short Answers I

#### 2 Marks

If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu.

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board Chapter 1 Mathematical Logic Long Answers II

#### 4 marks

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Write the following statements in symbolic form

Milk is white if and only if the sky is not blue

Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

**Use quantifiers to convert the following open sentences defined on N, into a true statement.**

n^{2} ≥ 1

Use quantifiers to convert the given open sentence defined on N into a true statement

3x – 4 < 9

Use quantifiers to convert the given open sentence defined on N into a true statement

Y + 4 > 6

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p

**Write the dual statement of the following compound statement.**

13 is prime number and India is a democratic country.

**Write the dual of the following**

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)

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

"If it snows, then they do not drive the car"

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board Chapter 1 Mathematical Logic Long Answers III

#### 4 marks

Examine whether the statement pattern

[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.

Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)

Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)

**With proper justification, state the negation of the following.**

(p ↔ q) v (~ q → ~r)

**Prepare truth table for (p ˄ q) ˅ ~ r**

(p ∧ q) ∨ ~ r

## Solutions for Chapter 1: Mathematical Logic

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board chapter 1 - Mathematical Logic

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board chapter 1 Mathematical Logic are Concept of Statements, Truth Value of Statement, Logical Connective, Simple and Compound Statements, Statement Patterns and Logical Equivalence, Tautology, Contradiction, and Contingency, Duality, Quantifier and Quantified Statements in Logic, Negations of Compound Statements, Converse, Inverse, and Contrapositive, Algebra of Statements, Application of Logic to Switching Circuits.

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