# 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)

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:

```x1z1= max(min(0.7, 0.9), min(0.5, 0.1))
= max(0.7 0.1)
= 0.7
x1z2= max(min(0.7, 0.6), min(0.5, 0.7))
= max(0.6, 0.5)
= 0.6
x1z3= max(min(0.7, 0.2), min(0.5, 0.5))
= max(0.2, 0.5)
= 0.5
x2z1= max(min(0.8, 0.9), min(0.4, 0.1))
= max(0.8, 0.1)
= 0.8
x2z2= max(min(0.8, 0.6), min(0.4, 0.7))
= max(0.6, 0.4)
= 0.6
x3z3= 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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