The $$2's$$ complement representation of $${\left( { - 539} \right)_{10}}$$ in hexadecimal is

Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular

Which of the following statements is correct?

Let $$f:\,A\, \to B$$ be a function, and let E and F be subsets of A. Consider the following statements about images.

$$S1:\,f\,\left( {E\, \cup \,F} \right)\, = \,f\left( E \right)\, \cup \,f\,\left( F \right)$$
$$S2:\,f\,\left( {E\, \cap \,F} \right)\, = \,f\left( E \right)\, \cap \,f\,\left( F \right)$$
Which of the following is true about S1 and S2?

Consider the following statements:

S1: There exist infinite sets A, B, C such that
$$A\, \cap \left( {B\, \cup \,C} \right)$$ is finite.
S2: There exist two irrational numbers x and y such that (x + y) is rational.
Which of the following is true about S1 and S2?