Chapter 1: Mathematical Logic
EXERCISE 1.1
Balbharati solutions for Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
EXERCISE 1.1Q 1 PAGE 2
Exercise 1.1 | Q 1 | Page 2
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
A triangle has ‘n’ sides
SOLUTION
It is an open sentence. Hence, it is not a statement.
[Note: Answer given in the textbook is ‘it is a statement’. However, we found that ‘It is not a statement’.]
EXERCISE 1.1Q 2 PAGE 2
Exercise 1.1 | Q 2 | Page 2
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The sum of interior angles of a triangle is 180°
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 3 PAGE 2
Exercise 1.1 | Q 3 | Page 2
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
You are amazing!
SOLUTION
It is an exclamatory sentence. Hence, it is not a statement.
EXERCISE 1.1Q 4 PAGE 2
Exercise 1.1 | Q 4 | Page 2
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
Please grant me a loan.
SOLUTION
It is a request. Hence, it is not a statement.
EXERCISE 1.1Q 5 PAGE 2
Exercise 1.1 | Q 5 | Page 2
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
√-4 is an irrational number.
SOLUTION
It is a statement which is false. Hence, it’s truth value is F.
EXERCISE 1.1Q 6 PAGE 2
Exercise 1.1 | Q 6 | Page 2
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
SOLUTION
It is a statement which is false. Hence, it’s truth value if F.
EXERCISE 1.1Q 7 PAGE 3
Exercise 1.1 | Q 7 | Page 3
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
He is an actor.
SOLUTION
It is an open sentence. Hence, it is not a statement.
EXERCISE 1.1Q 8 PAGE 3
Exercise 1.1 | Q 8 | Page 3
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
Did you eat lunch yet?
SOLUTION
It is an interrogative sentence. Hence, it is not a statement.
EXERCISE 1.1Q 9 PAGE 3
Exercise 1.1 | Q 9 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Have a cup of cappuccino.
SOLUTION
It is an imperative sentence, hence it is not a statement.
EXERCISE 1.1Q 10 PAGE 3
Exercise 1.1 | Q 10 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
(x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 11 PAGE 3
Exercise 1.1 | Q 11 | Page 3
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
Every real number is a complex number.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 12 PAGE 3
Exercise 1.1 | Q 12 | Page 3
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
1 is a prime number.
SOLUTION
It is a statement which is false. Hence, it’s truth value is F.
EXERCISE 1.1Q 13 PAGE 3
Exercise 1.1 | Q 13 | Page 3
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
With the sunset the day ends.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 14 PAGE 3
Exercise 1.1 | Q 14 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 ! = 0
SOLUTION
It is a statement which is false. Hence, it’s truth value is F.
[Note: Answer in the textbook is incorrect]
EXERCISE 1.1Q 15 PAGE 3
Exercise 1.1 | Q 15 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
3 + 5 > 11
SOLUTION
It is a statement which is false. Hence, it’s truth value is F.
EXERCISE 1.1Q 16 PAGE 3
Exercise 1.1 | Q 16 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number π is an irrational number.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
[Note: Answer in the textbook is incorrect]
EXERCISE 1.1Q 17 PAGE 3
Exercise 1.1 | Q 17 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 - y2 = (x + y)(x - y) for all x, y ∈ R.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 18 PAGE 3
Exercise 1.1 | Q 18 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number 2 is the only even prime number.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 19 PAGE 3
Exercise 1.1 | Q 19 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Two co-planar lines are either parallel or intersecting.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 20 PAGE 3
Exercise 1.1 | Q 20 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number of arrangements of 7 girls in a row for a photograph is 7!.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 21 PAGE 3
Exercise 1.1 | Q 21 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Give me a compass box.
SOLUTION
It is an imperative sentence. Hence, it is not a statement.
EXERCISE 1.1Q 22 PAGE 3
Exercise 1.1 | Q 22 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Bring the motor car here.
SOLUTION
It is an imperative sentence. Hence, it is not a statement.
EXERCISE 1.1Q 23 PAGE 3
Exercise 1.1 | Q 23 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
It may rain today.
SOLUTION
It is an open sentence. Hence, it is not a statement.
EXERCISE 1.1Q 24 PAGE 3
Exercise 1.1 | Q 24 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
SOLUTION
It is a statement which is true. Hence, it’s truth value is T.
EXERCISE 1.1Q 25 PAGE 3
Exercise 1.1 | Q 25 | Page 3
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Can you speak in English?
SOLUTION
It is an interrogative sentence. Hence, it is not a statement.
