1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the following Hasse diagrams.
GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 43 English 1
GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 43 English 2
GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 43 English 3
GATE CSE 2007 Discrete Mathematics - Set Theory & Algebra Question 43 English 4

Which all of the above represent a lattice?

A
(i) and (iv) only
B
(ii) and (iii) only
C
(iii) only
D
(i), (ii) and (iv) only
2
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
A partial order P is defined on the set of natural numbers as following. Herw x/y denotes integer division.
i) (0, 0) $$ \in \,P$$.
ii) (a, b) $$ \in \,P$$ if and only a %
$$10\, \le $$ b % 10 and
)a/10, b/10) $$ \in \,P$$.

Consider the following ordered pairs:
$$\matrix{ {i)\,\,\,(101,\,22)} & {ii)\,\,\,(22,\,\,101)} \cr {iii)\,\,\,(145,\,\,265)} & {iv)\,\,\,(0,\,153)} \cr } $$
Which of these ordered pairs of natural numbers are comtained in P?

A
(i), (iii) and (iv)
B
(ii) and (iv)
C
(i) and (iv)
D
(iii) and (iv)
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the set S = {a, b, c, d}. Consider the following 4 partitions $$\,{\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}$$ on $$S:\,{\pi _1} = \left\{ {\overline {a\,b\,c\,d} } \right\},\,{\pi _2} = \left\{ {\overline {a\,b\,} ,\,\overline {c\,d} } \right\},\,{\pi _3} = \left\{ {\overline {a\,b\,c\,} ,\,\overline d } \right\},\,{\pi _4} = \left\{ {\overline {a\,} ,\,\overline b ,\,\overline c ,\,\overline d } \right\}.$$ Let $$ \prec $$ be the partial order on the set of partitions $$S' = \{ {\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}\} $$ defined as follows: $${\pi _i} \prec \,\,{\pi _j}$$ if and only if $${\pi _i} $$ refines $${\pi _j}$$. The poset diagram for $$(S',\, \prec )$$ is
A
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 44 English Option 1
B
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 44 English Option 2
C
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 44 English Option 3
D
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 44 English Option 4
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let E, F and G be finite sets.
Let $$X = \,\left( {E\, \cap \,F\,} \right)\, - \,\left( {F\, \cap \,G\,} \right)$$
and $$Y = \,\left( {E\, - \left( {E\, \cap \,G} \right)} \right)\, - \,\left( {E\, - \,F\,} \right)$$. Which one of the following is true?
A
$$X\, \subset \,Y$$
B
$$X\, \supset \,Y$$
C
$$X\, = \,Y$$
D
$$X\, - \,Y\, \ne \,\emptyset \,\,and\,\,X\, - \,Y\, \ne \,\emptyset \,\,$$
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