Q49 / 125 · BITSAT 2017 · Mathematics

Let A={1,2,3,4,5} and R be a relation defined by R={(x,y):x,y∈A,x+y=5}. Then, R is

  • A
    reflexive and symmetric but not transitive
  • B
    an equivalence relation
  • Correct answer
    C
    neither reflexive nor transitive
  • D
    neither reflexive nor symmetric but transitive

Solution

We first write the elements of the set R.

i.e. R={(1,4),(4,1),(2,3),(3,2)}

Since, (1,1)∉R⇒R is not reflexive. 

Now as,(1,4)∈R⇒(4,1)∈R and (2,3)∈R

⇒ (3,2)∈R

So, R is symmetric 

Now, (1,4)∈R and (4,1)∈R

Thus, R is not transitive.

Hence, R is symmetric but neither reflexive nor transitive.

Hence, the correct answer is option: 'C'.

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