# UGC-NET | UGC NET CS 2016 July – III | Question 64

Let R and S be two fuzzy relations defined as:

and

Then, the resulting relation, T, which relates elements of universe X to elements of universe Z using max-min composition is given by**(A)** (1)**(B)** (2)**(C)** (3)**(D)** (4)**Answer:** **(D)****Explanation:** Since x is related to y and y is related to z, to relate universe x and universe z we have to compute max-min composition:

x_{1}z_{1}= max(min(0.7, 0.9), min(0.5, 0.1)) = max(0.7 0.1) = 0.7 x_{1}z_{2}= max(min(0.7, 0.6), min(0.5, 0.7)) = max(0.6, 0.5) = 0.6 x_{1}z_{3}= max(min(0.7, 0.2), min(0.5, 0.5)) = max(0.2, 0.5) = 0.5 x_{2}z_{1}= max(min(0.8, 0.9), min(0.4, 0.1)) = max(0.8, 0.1) = 0.8 x_{2}z_{2}= max(min(0.8, 0.6), min(0.4, 0.7)) = max(0.6, 0.4) = 0.6 x_{3}z_{3}= max(min(0.8, 0.2), min(0.4, 0.5)) = max(0.2, 0.4) = 0.4

So, option (C) is correct.

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