# Mathematics and Statistics 1 | Mathematical Logic | Textbook Excercise Solution

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q1) A triangle has "n" sides

Solution :- It is an open sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q2) The sum of interior angles of a triangle is 180�

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q3) You are amazing!

Solution :- It is an exclamatory sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q4) Please grant me a loan.

Solution :- It is a request. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q5)

## √-4  is an irrational number.

Solution :- It is a statement which is false. Hence, it is truth value is F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q6)

## x2 − 6x + 8 = 0 implies x = −4 or x = −2.

Solution :- It is a statement which is false. Hence, it is truth value if F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q7) He is an actor.

Solution :- It is an open sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q8) Did you eat lunch yet?

Solution :- It is an interrogative sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q9) Have a cup of cappuccino.

Solution :- It is an imperative sentence, hence it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q10)

## (x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q11) Every real number is a complex number.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q12) 1 is a prime number.

Solution :- It is a statement which is false. Hence, it is truth value is F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q13) With the sunset the day ends.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q14)

## 1 ! = 0

Solution :- It is a statement which is false. Hence, it is truth value is F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q15)

## 3 + 5 > 11

Solution :- It is a statement which is false. Hence, it is truth value is F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q16)

## The number π is an irrational number.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q17)

## x2 - y2 = (x + y)(x - y) for all x, y ∈ R.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q18) The number 2 is the only even prime number.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q19) Two co-planar lines are either parallel or intersecting.

Solution :- It is a statement which is true. Hence, it is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q20)

## 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 is truth value is T.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q21) Give me a compass box.

Solution :- It is an imperative sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q22) Bring the motor car here.

Solution :- It is an imperative sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q23) It may rain today.

Solution :- It is an open sentence. Hence, it is not a statement.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q24)

## If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.

Solution :- It is a statement which is false. Hence, it is truth value is F.

State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(Q25) Can you speak in English?

Solution :- It is an interrogative sentence. Hence, it is not a statement.