## Suppose x and y are natural numbers, then the numberof ordered pairs (x,y) which satisfy [tex]x + y \leqslant 5[/

Question

Suppose x and y are natural numbers, then the number
of ordered pairs (x,y) which satisfy

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5 months 2021-07-18T23:56:57+00:00 2 Answers 0 views 0

4

Step-by-step explanation:

As x and y are natural numbers, the cannot be 0

so the possible pairs are

(4,1)

(1,4)

(2,3)

(3,2)

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2. Given : x + y ≤ 5 . also x and y are natural numbers .

taking x = 1 , Possible values of y,

• y = 1 => x + y = 1 + 1 = 2 < 5 . { since it is not given x ≠ y}
• y = 2 , => 1 + 2 < 5 .
• y = 3 => 1 + 3 < 5
• y = 4 => 1 + 4 ≤ 5

So, at x = 1 we gets 4 pairs .

now, at x = 2 ,

• y = 1 , => 2 + 1 < 5
• y = 2 , => 2 + 2 < 5
• y = 3 , => 2 + 3 ≤ 5 .

So, at x = 2 we gets 3 pairs .

similarly, at x = 3 ,

• y = 1, => 3 + 1 < 5
• y = 2, => 3 + 2 ≤ 5 .

So, at x = 3 we gets 2 pairs .

now, at x = 4,

• y = 1 => 4 + 1 ≤ 5 .

So, at x = 4 we gets 1 pairs .

then,

→ Total order of pairs = 4 + 3 + 2 + 1 = 10 (Ans.)