Test: Set Theory- 1 - UPSC

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
 

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.

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.

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

′/′ 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. 

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