A function λ, is defined by

λ(p,q)={(pq)2,irpq,p+q,ifp<q.

The value of the expression λ((3+2),(2+3))((2+1)) is

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Calculation:

Given function λ is defined as 

λ(p,q)={(pq)2,irpq,p+q,ifp<q.

Let the given expression be P,

P=λ((3+2),(2+3))((2+1))

Simplifying the terms inside λ and denominator, we get 

P=λ((1),(1))((1))

P=λ(1,1)1

For p ≥  q, λ (p, q) = (p - q)2 

Now p = q ⇒ λ (p, q) = (p - p)2 = 0;

⇒ λ (1, 1) = 0

Now the value of expression P will be 

P=01=0;

∴ P = 0

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