DM - Functions & Relations -Q7

+1 vote

We define a relation R on set consisting of the first 1000 positive integers  such that  R is    then |R| = ? (Where, for a set S, |S| is the cardinality of the set S )

reshown 6 days ago

+1 vote

matrix representation of $\text{R}$ will contain $1000 \times 1000$ cells.

$a + b \leq 1001$$(a > 0, b > 0)$

can also write above equation with dummy variable c,

$a + b + c =1001$$\left ( a > 0 , b > 0, c \geq 0 \right )$

$a + 1 + b + 1 + c = 1001$

$a + b + c = 999$

$\binom{999+3-1}{3-1} = \binom{1001}{2} = 500500$

answered 4 days ago by (112,390 points)