Riemann surface
matlab

Smith, J. (2018). Introduction to Mathematical Logic. Oxford University Press.

Brown, A. (2019). Mathematical Logic and Applications. Wiley.

Miller, R. (2020). Stochastic Methods in Mathematical Logic. Springer.

Johnson, L. (2021). Applications of Mathematical Logic in Computer Science. Cambridge University Press.

Chen, H. (2022). Advanced Topics in Mathematical Logic: Gödel’s Incompleteness Theorems and Model Theory. MIT Press.

State which of the following sentences are statements. Justify your answer. In case of the statements, write down the truth value.
i. The Sun is a star.
ii. May God bless you!
iii. The sum of interior angles of a triangle is $180^{\circ}$.
iv. Every real number is a complex number.
v. Why are you upset?
vi. Every quadratic equation has two real roots.

Solution:
i. It is a statement which is true, hence its truth value is ‘ $\mathrm{T}$ ‘.
ii. It is an exclamatory sentence, hence, it is not a statement.
iii. It is a statement which is true, hence its truth value is ‘ $\mathrm{T}$ ‘.
iv. It is a statement which is true, hence its truth value is ‘ $\mathrm{T}$ ‘.
v. It is an interrogative sentence, hence it is not a statement.
vi. It is a statement which is false, hence its truth value is ‘ $\mathrm{F}$ ‘.

vii. $\sqrt{-9}$ is a rational number.
viii. $x^2-3 x+2=0$, implies that $x=-1$ or $x=-2$.
ix. The sum of cube roots of unity is one.
x. Please get me a glass of water.
xi. He is a good person.
xii. Two is the only even prime number.
xiii. $\sin 2 \theta=2 \sin \theta \cos \theta$ for all $\theta \in R$.
xiv. What a horrible sight it was!

vii. It is a statement which is false, hence its truth value is ‘ $F$ ‘.
viii. It is a statement which is false, hence its truth value is ‘ $\mathrm{F}$ ‘.
ix. It is a statement which is false, hence its truth value is ‘ $F$ ‘.
x. It is an imperative sentence, hence it is not a statement.
xi. It is an open sentence, hence it is not a statement.
xii. It is a statement which is true, hence its truth value is ‘ $\mathrm{T}$ ‘.
xiii. It is a statement which is true, hence its truth value is ‘ $\mathrm{T}$ ‘.
xiv. It is an exclamatory sentence, hence it is not a statement.

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