Set Theory And Relations Test

Result

Set Theory And Relations Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

Let R be a relation on the set N of natural numbers defined by nRm ⇔ n is a factor of m (i.e., n|m). Then R is

A
Reflexive and symmetric

B
Transitive and symmetric

C
Equivalence

D
Reflexive, transitive but not symmetric

Solution

Since n | n for all n∈N, therefore R is reflexive. Since 2 | 6 but 6 | 2, therefore R is not symmetric.

Let n R m and m R p ⇒ n|m and m|p ⇒ n|p ⇒ nRp. So R is transitive.
Question 2
1 / -0

Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is

A
Less than n

B
Greater than or equal to n

C
Less than or equal to n

D
None of these

Solution

Since R is an equivalence relation on set A, therefore (a, a) ∈ R for all α ∈ R . Hence, R has at least n ordered pairs.
Question 3
1 / -0

Let X be a family of sets and R be a relation on X defined by ‘A is disjoint from B’. Then R is

A
Reflexive

B
Symmetric

C
Anti-symmetric

D
Transitive

Solution

Clearly, the relation is symmetric but it is neither reflexive nor transitive.