# GATE CSE 2001

 Question 1
Consider the following statements:

S1: The sum of two singular nxn matrices may be non-singular
S2: The sum of two nxn non-singular matrices may be singular.

Which of the following statements is correct?
 A S1 and S2 are both true B S1 is true, S2 is false C S1 is false, S2 is true D S1 and S2 are both false
Engineering Mathematics   Linear Algebra
Question 1 Explanation:
 Question 2
Consider the following relations:

R1(a,b) iff (a+b) is even over the set of integers
R2(a,b) iff (a+b) is odd over the set of integers
R3(a,b) iff a.b > 0 over the set of non-zero rational numbers
R4(a,b) iff |a - b| <= 2 over the set of natural numbers

Which of the following statements is correct?
 A R1 and R2 are equivalence relations, R3 and R4 are not B R1 and R3 are equivalence relations, R2 and R4 are not C R1 and R4 are equivalence relations, R2 and R3 are not D R1, R2, R3 and R4 are all equivalence relations
Discrete Mathematics   Relation
Question 2 Explanation:

 Question 3
Consider two well-formed formulas in prepositional logic.
$F1: \; P\Rightarrow \neg P$
$F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)$
Which of the following statements is correct?
 A F1 is satisfiable, F2 is valid B F1 unsatisfiable, F2 is satisfiable C F1 is unsatisfiable, F2 is valid D F1 and F2 are both satisfiable
Discrete Mathematics   Propositional Logic
Question 3 Explanation:
 Question 4
Consider the following two statements :
S1: {$0^{2n}|n\geq 1|$} is a regular language
S2 : {$0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|$} is a regular language
Which of the following statements is correct?
 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
Theory of Computation   Regular Language
Question 4 Explanation:
 Question 5
Which of the following statements true ?
 A If a language is context free it can be always be accepted by a deterministic push-down automaton. B The union of two context free language is context free. C The intersection of two context free language is context free D The complement of a context free language is context free
Theory of Computation   Context Free Language
Question 5 Explanation:

There are 5 questions to complete.