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

## 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.

MCQ

### 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

MCQ | Q 1

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

MCQ | Q 2

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

MCQ | Q 3

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

• Contingency

• Tautology

• None of these

MCQ | Q 4

Choose the correct alternative :

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

• Tautology

• Neither (i) not (ii)

• None of the these

MCQ | Q 5

Negation of p → (p ˅ ∼ q) is

• ∼ p → (∼ p ˅ q)

• p ˄ (∼ p ˄ q)

• ∼ p ˅ (∼ p ˅ ∼ q)

• ∼ p → (∼ p → q)

MCQ | Q 6

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

MCQ | Q 7

A biconditional statement is the conjunction of two ______ statements

• Negative

• Compound

• Connective

• Conditional

MCQ | Q 8

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

• Converse

• Contrapositive

• Inverse

• Alternative

MCQ | Q 9

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

• p ˄ q ˄ ∼ r

• (p ˄ q) ˅ r

• p ˅ q ˅ ∼ r

• (p v q) ˄ (r ˅ s)

MCQ | Q 10

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

Very Short Answers | Q 1

Find the negation of 10 + 20 = 30

Very Short Answers | Q 2

State the truth Value of x2 = 25

Very Short Answers | Q 3

Write the negation of p → q

Very Short Answers | Q 4

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

Very Short Answers | Q 5

State the truth value of (p ˅ ∼p)

Very Short Answers | Q 6

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

Short Answers I | Q 1.1

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

~ p ∧ (q ∨ ~ r)

Short Answers I | Q 1.2

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

(p ∧ ~r) ∧ (~q ∨ s)

Short Answers I | Q 2.1

Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu.

Short Answers I | Q 2.2

Write the following compound statements symbolically.

Triangle is equilateral or isosceles

Short Answers I | Q 3

Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”

Short Answers I | Q 4

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

Long Answers II | Q 1

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

Long Answers II | Q 2.1

Write the following statements in symbolic form

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

Long Answers II | Q 2.2

Write the following statements in symbolic form

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

Long Answers II | Q 2.3

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining

Long Answers II | Q 3.1

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

n2 ≥ 1

Long Answers II | Q 3.2

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

3x – 4 < 9

Long Answers II | Q 3.3

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

Y + 4 > 6

Long Answers II | Q 4

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Long Answers II | Q 5

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

Long Answers II | Q 6.1

Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.

Long Answers II | Q 6.2

Write the dual of the following

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

Long Answers II | Q 7

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

Long Answers III | Q 1

Examine whether the statement pattern

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

Long Answers III | Q 2

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

Long Answers III | Q 3

Without using truth table show that -

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

Long Answers III | Q 4

With proper justification, state the negation of the following.

(p ↔ q) v (~ q → ~r)

Long Answers III | Q 5

Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r

## 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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