1
GATE CSE 2015 Set 3
+1
-0.3
Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?
A
$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$
B
$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$
C
$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$
D
$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$
2
GATE CSE 2015 Set 2
Numerical
+1
-0
The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.
3
GATE CSE 2015 Set 2
+1
-0.3
Let $$𝑅$$ be the relation on the set of positive integers such that $$aRb$$ if and only if $$𝑎$$ and $$𝑏$$ are distinct and have a common divisor other than $$1.$$ Which one of the following statements about $$𝑅$$ is true?
A
$$𝑅$$ is symmetric and reflexive but not transitive
B
$$𝑅$$ is reflexive but not symmetric and not transitive
C
$$𝑅$$ is transitive but not reflexive and not symmetric
D
$$𝑅$$ is symmetric but not reflexive and not transitive
4
GATE CSE 2015 Set 1
+1
-0.3
For a set A, the power set of A is denoted by 2A. If A = {5, {6}, {7}}, which of the following options are TRUE?

I. $$\phi \in {2^A}$$
II. $$\phi \subseteq {2^A}$$
III. $$\left\{ {5,\left\{ 6 \right\}} \right\} \in {2^A}$$
IV. $$\left\{ {5,\left\{ 6 \right\}} \right\} \subseteq {2^A}$$

A
I and III only
B
II and III only
C
I, II and III only
D
I, II and IV only
GATE CSE Subjects
EXAM MAP
Medical
NEET