Which among A relation R is defined on N, the set of natural numbers, as R = {(a, b): a= b-3, b<5}. The ordered pair present in R is:the following is not an equivalence relation?: a) (3.6) b (0,3) c) (1,4)
Answers
Step-by-step explanation
Given a relation R=(1,2),(2,3) on the set of natural numbers, add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.
EASY
Share
Save
ANSWER
For the relation R to be reflexive, it is necessary that (n, n) ∈ R for every n ∈ N that is, R must have all pairs (1, 1), (2, 2), (3, 3),...........
For R to be symmetric, it must contain the pair (2, 1) and (3, 2) since the pairs (1, 2) and (2, 3) are already present.
For R to be transitive, it must contain the pair (1, 3) since (1, 2) and (2, 3) are already there. We must then also include the pair (3, 1) for symmetry. Hence the relation R' obtained from R by adding a minimum number of ordered pairs to R to make it an equivalence relation is
R
′
=(1,2).(2,1),(2,3),(3,2),(1,3),(3,1),(1,1),(2,2)
Answer:
It is given that , a= {1,5}, b={3,7} : r=(a,b) and a-b is multiple of 4.
We have to find relation r.
Solution : Consider the following pairs
(1,3)=1 -3= -2,
(1,7) = 1- 7 = -6
(5,3) = 5 -3 =2
(5,7) = 5 - 7 = -2
As , none of the pair (1,3),(1,7), (5,3),)(5,7) satisfies the condition that a-b is multiple of 4, where a= first element of ordered pair and b= Second element of ordered pair.
So→ [r(a, b) such that a-b is multiple of 4], does not form any kind of relation from a to b.
Step-by-step explanation: