Question

If N = 1000, (A) = 700, (B) = 400, (AB) = 50 then the data is​

Answer 1

Answer:

8

Step-by-step explanation:

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Answer 2

Given,

N = 1000, (A) = 700, (B) = 400, (AB) = 50

To Find,

Wheater data is consitent or inconsistent

Solution,

T0 check whether data is consistent or inconsitent we will find its values. if any value is negative then the data is inconsistent otherwise it is consistent data.

We know that, $N= (A) + (\alpha ) = (B) + (\beta )$

and also $(A) = (AB) + (A\beta )$

$(\alpha ) = (\alpha B) + (\alpha \beta )$

$(B) = (AB) + (\alpha B)$

$(\beta ) = (A\beta ) + (\alpha \beta )$

Putting values given in question in the formula we get,

In the $(A) = (AB) + (A\beta )$ equation, $700 = 50 + (A\beta )$

$(A\beta ) = 700-50 = 650$

In  $(B) = (AB) + (\alpha B)$ equation,

$(400) = 50 + (\alpha B)$

$(\alpha B)= 400-50 = 350$

In the $N= (A) + (\alpha ) = (B) + (\beta )$ equation,

$1000=700+ (\alpha )$

$(\alpha ) = 1000-700 = 300$

in same equation,

$N= (B) + (\beta )$

$1000= 400 + (\beta )$

$(\beta ) = 1000-400 = 600$

Now putting values in $(\alpha ) = (\alpha B) + (\alpha \beta )$

$300 = 350 + (\alpha \beta )$

$(\alpha \beta ) = -50$

Hence, $\alpha \beta$ is -50 which is negative so the data is inconsistent