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Test: Set Theory- 1


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Test: Set Theory- 1 - Question 1

Let R be a non-empty relation on a collection of sets defined by ARB if and only if A  ∩ B = Ø
Then (pick the TRUE statement) 

Detailed Solution for Test: Set Theory- 1 - Question 1

The correct answer is B asLet A={1,2,3
B={4,5} 
C={1,6,7}
now 
A∩B=∅ 
B∩C=∅
B∩C=∅ but 
A∩C≠∅
R is not transitive.

A∩A=A
R is not reflexive.

A∩B=B∩A
R is symmetric
So, 
A is false as 
R is not reflexive or transitive
B is true.
C is false because 
R is not transitive or reflexive
D is false because 
R is symmetric
 

Test: Set Theory- 1 - Question 2

The binary relation S =  Φ (empty set) on set A = {1, 2,3}  is

Detailed Solution for Test: Set Theory- 1 - Question 2

Explanation:

  • Reflexive : A relation is reflexive if every element of set is paired with itself. Here none of the element of A is paired with themselves, so S is not reflexive.
  • Symmetric : This property says that if there is a pair (a, b) in S, then there must be a pair (b, a) in S. Since there is no pair here in S, this is trivially true, so S is symmetric.
  • Transitive : This says that if there are pairs (a, b) and (b, c) in S, then there must be pair (a,c) in S. Again, this condition is trivially true, so S is transitive.

    Thus, option (D) is correct.

Test: Set Theory- 1 - Question 3

Which of the following sets are null sets ?

Detailed Solution for Test: Set Theory- 1 - Question 3

There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø.

Test: Set Theory- 1 - Question 4

Number of subsets of a set of order three is

Detailed Solution for Test: Set Theory- 1 - Question 4

Number of subset = 2n
order 3 = 23
⇒ 8

Test: Set Theory- 1 - Question 5

"n/m" means that n is a factor of m, then the relation T is

Detailed Solution for Test: Set Theory- 1 - Question 5

′/′ is reflexive since every natural number is a factor of itself that in n/n for n∈N.
′/′ is transitive if n is a factor of m and m is a factor of P, then n is surely a factor of P.
However, ′/′ is not symmetric.
example, 2 is a factor of 4 but 4 is not a factor of 2. 

Test: Set Theory- 1 - Question 6

The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

Test: Set Theory- 1 - Question 7

If A and B are sets and A∪ B= A  ∩ B, then

Test: Set Theory- 1 - Question 8

Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then

Detailed Solution for Test: Set Theory- 1 - Question 8

Let S = S1 ∪ S2 ∪ S3 ∪ .... Sn . 
For S to be infinite set, atleast one of sets Si must be infinite, 
if all Si were finite, then S will also be finite.

Test: Set Theory- 1 - Question 9

If X and Y are two sets, then X  ∩ (Y  ∪ X) C equals

Detailed Solution for Test: Set Theory- 1 - Question 9

Test: Set Theory- 1 - Question 10

If  f : X -> Y and a, b  ⊆ X, then f (a  ∩ b) is equal to

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