Chapter 1 - Mathematical Logic [Latest edition]
Balbharati solutions for Mathematics and Statistics 1 (Commerce)
12th Standard HSC Maharashtra State Board
State which of the following sentences is a statement. Justify your answer if it is a statement. Write down its truth value.
QUESTION
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’.]
QUESTION
The sum of interior angles of a triangle is 180°
It is a statement which is true. Hence, it’s truth value is T.
QUESTION
You are amazing!
It is an exclamatory sentence. Hence, it is not a statement.
QUESTION
Please grant me a loan.
It is a request. Hence, it is not a statement.
QUESTION
It is a statement which is false. Hence, it’s truth value is F.
QUESTION
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
QUESTION
He is an actor.
QUESTION
Did you eat lunch yet?
QUESTION
Have a cup of cappuccino.
QUESTION
(x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.
QUESTION
Every real number is a complex number.
QUESTION
1 is a prime number.
QUESTION
With the sunset the day ends.
QUESTION
1 ! = 0
QUESTION
3 + 5 > 11
QUESTION
The number π is an irrational number.
QUESTION
x2 - y2 = (x + y)(x - y) for all x, y ∈ R.
QUESTION
The number 2 is the only even prime number.
QUESTION
Two co-planar lines are either parallel or intersecting.
QUESTION
The number of arrangements of 7 girls in a row for a photograph is 7!.
QUESTION
Give me a compass box.
QUESTION
Bring the motor car here.
QUESTION
It may rain today.
QUESTION
If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
QUESTION
Can you speak in English?