GATE CSE 2004 | GATE CSE Year Wise Previous Years Questions

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GATE CSE 2004

MCQ (Single Correct Answer)

-0.3

Consider the binary relation: $$S = \left\{ {\left( {x,y} \right)|y = x + 1\,\,and\,\,x,y \in \left\{ {0,1,2,...} \right\}} \right\}$$

The reflexive transitive closure of $$S$$ is

$$\left\{ {\left( {x,y} \right)|y > x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$

$$\left\{ {\left( {x,y} \right)|y \ge x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$

$$\left\{ {\left( {x,y} \right)|y < x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$

$$\left\{ {\left( {x,y} \right)|y \le x\,\,\,and\,\,\,x,y \in \left\{ {0,1,2,.....} \right\}} \right\}$$

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}

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

The following is the incomplete operation table of a 4-element group. GATE CSE 2004 Discrete Mathematics - Set Theory & Algebra Question 103 English

GATE CSE 2004 Discrete Mathematics - Set Theory & Algebra Question 103 English

The last row of the table is

$$\matrix{ c & a & e & b \cr } $$

$$\matrix{ c & b & a & e \cr } $$

$$\matrix{ c & b & e & a \cr } $$

$$\matrix{ c & e & a & b \cr } $$

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

Two n bit binary stings, S1 and, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings different) is equal to d is

$$^n{C_d}/{2^n}$$

$$^n{C_d}/{2^d}$$

$$d/{2^n}$$

$$1/{2^d}$$

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