DM - Functions & Relations -Q7

+1 vote

We define a relation R on set A = \{1, 2, 3, . . . , 1000\} consisting of the first 1000 positive integers  such that  R is  \{(a, b) | a + b \leq 1001\}   then |R| = ? (Where, for a set S, |S| is the cardinality of the set S )

asked Jun 24 in Discrete Maths by gbeditor (44,500 points)
reshown 6 days ago by gbeditor

1 Answer

+1 vote
 
Best answer

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 deepak-gatebook (112,390 points)
Answer:
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