# Exercise 1.1 (1)

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

i) A triangle has ‘n’ sides
Ans: It is a Statement which is false. Hence, it truth value is F.

ii) The sum of interior angles of a triangle is 180°
Ans: It is a Statement which is true. Hence, it’s truth value is T.

iii) You are amazing!
Ans: It is an Exclamatory Sentence, Hence, it is not a statement.

iv) Please grant me a loan.
Ans: It is a request. Hence, it is not a statement.

v) √−4 is an irrational number.
Ans:  It is a Statement which is false, Hence, it’s truth value is F

vi) x2 − 6x + 8 = 0 implies x = −4 or x = −2.
Ans: It is a Statement which is False. Hence, it’s truth value is F

vii) He is an actor.
Ans: It is an open sentence. Hence, it is not a statement.

viii) Did you eat lunch yet?
Ans: It is an interrogative sentence. Hence, it is not a statement.

ix) Have a cup of cappuccino.
Ans: It is an imperative sentence. Hence, it is not a statement.

x) (x + y)2 = x2 + 2xy + y2 for all x, y ∈ R.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xi) Every real number is a complex number.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xii) 1 is a prime number.
Ans:  It is a Statement which is False. Hence, it’s truth value is F

xiii) With the sunset the day ends.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xiv) 1 ! = 0
Ans: It is a Statement which is False. Hence, it’s truth value is F

xv) 3 + 5 > 11
Ans: It is a Statement which is False. Hence, it’s truth value is F

xvi) The number Π is an irrational number.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xvii) x2 − y2 = (x + y) (x − y) for all x, y ∈ R.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xviii) The number 2 is the only even prime number.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xix) Two co-planar lines are either parallel or intersecting.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xx) The number of arrangements of 7 girls in a row for a photograph is 7!.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xxi) Give me a compass box.
Ans: It is an imperative sentence. Hence, it is not a statement.

xxii) Bring the motor car here.
Ans: It is an imperative sentence. Hence, it is not a statement.

xxiii) It may rain today.
Ans: It is a Open Sentence.. Hence, it is not a statement

xxiv) If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
Ans: It is a Statement which is True. Hence, it’s truth value is T

xxv) Can you speak in English?
Ans: It is a Interrogative Sentence. Hence, it is not a statement