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34.1k views
in Sets, Relations and Functions by (50.2k points)
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Let A = {1, 2, 3} and consider the relation

R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is 

A. reflexive but not symmetric

B. reflexive but not transitive 

C. symmetric and transitive 

D. neither symmetric, nor transitive

1 Answer

+1 vote
by (48.8k points)
selected by
 
Best answer

Given that, A = {1, 2, 3} and

R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}.

Now,

R is reflexive ∵ (1,1),(2,2),(3,3) ∈ R

R is not symmetric ∵ (1,2),(2,3),(1,3) ∈ R but (2,1),(3,2),(3,1) ∉ R

R is transitive ∵ (1,2) ∈ R and (2,3) ∈ R ⇒ (1,3) ∈ R

Thus, R is reflexive, transitive but not symmetric.

Hence, option ‘A’ is correct.

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