1
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-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 42 English
A
not a lattice
B
a lattice but not a distributive lattice
C
a distributive lattice but not a Boolean algebra
D
a Boolean algebra
2
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-0.3
Let $$A$$, $$B$$ and $$C$$ be non-empty sets and let $$X = (A - B) - C$$ and $$Y = (A - C) - (B - C)$$

Which one of the following is TRUE?

A
$$X = Y$$
B
$$X \subset Y$$
C
$$Y \subset X$$
D
None of these
3
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-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 $$g$$?
A
$$g$$ is onto $$ \Rightarrow $$ $$h$$ is onto
B
$$h$$ is onto $$ \Rightarrow $$$$f$$ is onto
C
$$h$$ is onto $$ \Rightarrow $$ $$g$$ is onto
D
$$h$$ is onto $$ \Rightarrow $$ $$f$$ and $$g$$ are onto
4
GATE CSE 2004
MCQ (Single Correct Answer)
+1
-0.3
Let $${R_1}$$ be a relation from $$A = \left\{ {1,3,5,7} \right\}$$ to $$B = \left\{ {2,4,6,8} \right\}$$ and $${R_2}$$ be another relation from $$B$$ to $$C$$ $$ = \left\{ {1,2,3,4} \right\}$$ as defined below:

i) An element $$x$$ in $$A$$ is related to an element $$y$$ in $$B$$ (under $${R_1}$$) if $$ x + y $$ is divisible by $$3$$.
ii) An element EExEE in $$B$$ is related to an elements $$y$$ in $$C$$ (under $${R_2}$$) if $$x + y$$ is even but not divisible by $$3$$.

Which is the composite relation $$R1R2$$ from $$A$$ to $$C$$?

A
$${R_1}\,{R_2}\, = \,\left\{ {\left( {1,2} \right),\,\left( {1,4} \right),\,\left( {3,3} \right),\,\left( {5,4} \right),\,\left( {7,3} \right)} \right\}$$
B
$${R_1}\,{R_2}\, = \,\left\{ {\left( {1,2} \right),\,\left( {1,3} \right),\,\left( {3,2} \right),\,\left( {5,2} \right),\,\left( {7,3} \right)} \right\}$$
C
$${R_1}\,{R_2}\, = \,\left\{ {\left( {1,2} \right),\,\left( {3,2} \right),\,\left( {3,4} \right),\,\left( {5,4} \right),\,\left( {7,2} \right)} \right\}$$
D
$${R_1}\,{R_2}\, = \,\left\{ {\left( {3,2} \right),\,\left( {3,4} \right),\,\left( {5,1} \right),\,\left( {5,3} \right),\,\left( {7,1} \right)} \right\}$$
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