UGC NET CSE | June 2013 | Part 2 | Question: 34

Question

The relation “devides” on a set of positive integers is_____

• A. Symmetric and transitive
• B. Anti symmetric and transitive
• C. Symmetric only
• D. Transitive only

Comments

Symmetric

Answer 1

Relation “divides” on set of positive integers is transitive. Suppose a divides b, and b divides c. Then there are exist positive integers m and n, so that b = ma and c = nb.

Therefore c= nma, then a divides c. So, relation “divides” is transitive

Relation "divides" on set of positive number is Anti Symmetric.

Suppose if x is divisor of y then y can't be a divisor of x until x=y.

 Hence,Option(B)Anti Symmetric and Transitive.

Comments

Example:- [ D₃₀ ; / ]

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@LeenSharma if domain is set of +ve real number , will it be Antisymmetric relation?

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what if set of all integers is given?

Answer 2

Anti Symmertic and transtive relation both are the best option.

Option B.

Transitive relation::

If a relation R is such that aRb,bRc then aRc for all a,b and c belong to R.

So all operation like >,<,subset,superset,/ are transitive relation.

Anti Symmetric relation::
A relation is called as anti Symmetric relation if and only if aRb and bRa then a==b and there exist no order pair.

Apply above intuition and u will get option B as right option.

Answer 3

Divide is symmetric for some numbers eg (4,4) Divide is antisymmetric for some numbers eg(10,2) 10/2 is 5 by 2/10 is not integer. Divide is transitive. If a divides b and b divides c then we can say a divides c So answer is D

Comments

it should be anti-symmetric.A relation 'R' said to be anti-symmetric if xRy and yRx then  x=y ∀x,y∈A(any set)

it means R(x,y) with x≠y then R(y,x) must not hold.

 

for your example (10,2) is in relation and (2,10) is not present in relation.Right?