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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 96 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

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)

-0.3

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)

-0.3

The number of different $$n$$ $$x$$ $$n$$ symmetric matrices with each elements being either $$0$$ or $$1$$ is (Note: power ($$2,$$ $$x$$) is same as $${2^x}$$)

power $$(2, n)$$

power $$\left( {2,\,{n^2}} \right)$$

$$\left( {2,\left( {{n^2} + n} \right)/2} \right)$$

power $$\left( {2,\left( {{n^2} - n} \right)/2} \right)$$

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