Question

Let \(A=\{-3,-2,-1,0,1,2,3\}.\) A relation R is defined such that x R y iff \(y=\max \{x, 1\}.\)

Number of elements required to make it reflexive is I, number of elements required to make it symmetric is m and number of elements in the relation R is n. Then value of l + m + n is equal to

Answer 1

Answer is: 15 

\(R=\{(-3,1),(-2,1),(-1,1),(0,1),(1,1),(2,2),(3,3\}\)

\(\therefore I=4 i.e., (-3,-3),(-2,-2),(-1,-1),(0,0)\)

m = 4 i.e., (1,-3), (1, -2), (1, -1), (1, 0)

n = 7

l + m + n = 15