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?
| A. | Only S1, is correct |
| B. | Only S2 is correct |
| C. | Both S1 and S2 are correct |
| D. | None of S1 and S2 is correct |
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Option: A Explanation : Click on Discuss to view users comments. |
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
| A. | |
| B. | f -1(x,y) = (x - y, x + y) |
| C. | |
| D. | f-1(x,y)=[2(x - y), 2(x + y)] |
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Option: C Explanation : Click on Discuss to view users comments. |
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 Si and S2?
| A. | Only S1 is correct |
| B. | Only S2 is correct |
| C. | Both S1 and S2 are correct |
| D. | None of S1 and S2 are correct |
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Option: A Explanation : Click on Discuss to view users comments. |
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
| A. | reflexive, symmetric and transitive |
| B. | neither reflexive, nor irreflexive but transitvie |
| C. | irreflexive, symmetric and transitive |
| D. | irreflexive and antisymmetric |
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Option: B Explanation : Click on Discuss to view users comments. |
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
| A. | │x│ = 1, │y│ = 97 |
| B. | │x│ = 97, │y│= 1 |
| C. | │x│ = 97, │y│= 97 |
| D. | none of these |
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Option: A Explanation : Click on Discuss to view users comments. |
