1
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
2
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
3
GATE CSE 2016 Set 1
Numerical
+2
-0
A function $$f:\,\,{N^ + } \to {N^ + },$$ defined on the set of positive integers $${N^ + },$$ satisfies the following properties: $$$\eqalign{ & f\left( n \right) = f\left( {n/2} \right)\,\,\,\,if\,\,\,\,n\,\,\,\,is\,\,\,\,even \cr & f\left( n \right) = f\left( {n + 5} \right)\,\,\,\,if\,\,\,\,n\,\,\,\,is\,\,\,\,odd \cr} $$$

Let $$R = \left\{ i \right.|\exists j:f\left( j \right) = \left. i \right\}$$ be the set of distinct values that $$f$$ takes. The maximum possible size of $$R$$ is _____________________.

Your input ____
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?
A
Both reflexive and symmetric
B
Reflexive but not symmetric
C
Not reflexive but symmetric
D
Neither reflexive nor symmetric
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