GATE CSE 2005 | Set Theory & Algebra Question 55 | Discrete Mathematics

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets $${S_1}$$ and $${S_2}$$ in C, either $${S_1}\, \subset \,{S_2}$$ or $${S_2}\, \subset \,{S_1}$$. What is the maximum cardinality of C?

n + 1

$${2^{n - 1}}\, + \,1$$

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. Given that h is an onto function which one of the following is TRUE?

f and g should both be onto functions

f should be onto but g need not be into

g should be onto but f need not be onto

both f and need not be onto

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations

$$R\, \cup \,S\,$$ is an equivalence relations

$$R\, \cap \,S$$ is an equivalence relations

Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

The inclusion of which of the following sets into

S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4},
{1, 2, 3, 4, 5} }
Is necessary and sufficient to make S a complete lattice under the partial order defined by set containment?

{1}

{1}, {2, 3}

{1}, {1, 3}

{1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}

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