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

Correct Answer is : symmetric but neither reflexive nor transitive

reflexive and symmetric but not transitive

neither reflexive nor symmetric but transitive

Correct Answer is : symmetric but neither reflexive nor transitive

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BITSAT 2017 Slot 2 Solved Paper

Section: Mathematics

Question : 114 of 150

Marks: +1, -0

Let

A=\{1,2,3,4,5\}

R

R=\{(x, y): x, y \in A, x+y=5\} .

R

Solution:

We first write the elements of the set

R

. i.e.

R=\{(1,4),(4,1),(2,3),(3,2)\}

Since,

(1,1) \notin R \Rightarrow R

is not reflexive.

Now as,

(1,4) \in R \Rightarrow (4,1) \in R

and

(2,3) \in R

\Rightarrow

(3,2) \in R

So,

R

is symmetric

Now,

(1,4) \in R

and

(4,1) \in R

\Rightarrow (1,1) \in R

Thus,

R

is not transitive.

Hence,

R

is symmetric but neither reflexive nor transitive.

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