1
GATE CSE 2016 Set 2
Numerical
+1
-0
The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .
Your input ____
2
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A binary relation $$R$$ on $$N \times N$$ is defined as follows: $$(a,b)R(c,d)$$ if $$a \le c$$ or $$b \le d.$$ Consider the following propositions:

$$P:$$ $$R$$ is reflexive
$$Q:$$ $$R$$ is transitive

Which one of the following statements is TRUE?

A
Both $$P$$ and $$Q$$ are true
B
$$P$$ is true and $$Q$$ is false
C
$$P$$ is false and $$Q$$ is true
D
Both $$P$$ and $$Q$$ are false
3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider a set $$U$$ of $$23$$ different compounds in a Chemistry lab. There is a subset $$S$$ of $$U$$ of $$9$$ compounds, each of which reacts with exactly $$3$$ compounds of $$U.$$ Consider the following statements:

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ At least one compound in $$U \ S$$ reacts with an odd number of compounds.
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,$$ Each compound in $$U \ S$$ reacts with an even number of compounds.

Which one of the above statements is ALWAYS TRUE?

A
Only $${\rm I}$$
B
Only $${\rm II}$$
C
Only $${\rm III}$$
D
None
4
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following well-formed formulae in predicate calculus is NOT valid?
A
$$\left( {\forall xp\left( x \right) \vee \forall xq\left( x \right)} \right) \Rightarrow \left( {\exists x\neg p\left( x \right) \vee \forall xq\left( x \right)} \right)$$
B
$$\left( {\exists xp\left( x \right) \vee \exists xq\left( x \right)} \right) \Rightarrow \exists x\left( {p\left( x \right) \vee q\left( x \right)} \right)$$
C
$$\exists x\left( {p\left( x \right) \wedge q\left( x \right)} \right) \Rightarrow \left( {\exists xp\left( x \right) \wedge \exists xq\left( x \right)} \right)$$
D
$$\forall x\left( {p\left( x \right) \vee q\left( x \right)} \right) \Rightarrow \left( {\forall xp\left( x \right) \vee \forall xq\left( x \right)} \right)$$
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