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Discrete Maths - Sets

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121. Consider the following statements :
S1 : There exist infinite sets A, B, C such that A ∩ (B ∪ C) 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?

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122. Let R denote the set of real numbers.
 Let f: R x R → R x R be a bijective function deined by f(x, y) = (x + y, x - y).

The inverse function off is given by

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123. Let f : A → B be a function, and let E and F be  subsets of A.
Consider following statements about images.

S1 : f(E ∪ F) = f(E) ∪ f(F)

S2 : f(E ∩ F) = f(E) ∩ f(F)
Which of the following is TRUE about S1 and S2?

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124. The binary relation
r = {(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2),(3,3), (3, 4)}
on the set A = {1, 2, 3, 4} is

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125. Let x and y are sets and I x I and l y I are their respective cardinalities. It is given that there are exactly 97 functions from x to y. From this one can conclude that

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