GATE CSE 2005 | Set Theory & Algebra Question 58 | Discrete Mathematics

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

Let $$f$$ be a function from a set $$A$$ to a set $$B$$, $$g$$ a function from $$B$$ to $$C$$, and $$h$$ a function from $$A$$ to $$C$$, such that $$h\left( a \right) = g\left( {f\left( a \right)} \right)$$ for all $$a \in A$$. Which of the following statements is always true for all such functions $$f$$ and $$g$$?

$$g$$ is onto $$ \Rightarrow $$ $$h$$ is onto

$$h$$ is onto $$ \Rightarrow $$$$f$$ is onto

$$h$$ is onto $$ \Rightarrow $$ $$g$$ is onto

$$h$$ is onto $$ \Rightarrow $$ $$f$$ and $$g$$ are onto

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

The following is the Hasse diagram of the poset $$\left[ {\left\{ {a,b,c,d,e} \right\}, \prec } \right]$$

The poset is:

GATE CSE 2005 Discrete Mathematics - Set Theory & Algebra Question 39 English

not a lattice

a lattice but not a distributive lattice

a distributive lattice but not a Boolean algebra

a Boolean algebra

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

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

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

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

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