UGC-NET | UGC NET CS 2018 Dec – II | Question 46

The relation​ ​ ≤ and < on a boolean algebra are defined as :

x ≤ y and only if x ∨ y = y
x < y means x ≤ y but x ≠ y
x ≥ y means y ≤ x and
x > y means y < x  

Consider the above definitions, which of the following is not true in the boolean algebra ?

• (i) If x ≤ y and y ≤ z, then x ≤ z
• (ii) If x ≤ y and y ≤ x, then x=y
• (iii) If x < y and y < z, then x ≤ y
• (iv) If x < y and y < z, then x < y

(A) (iv) only
(B) (iii) only
(C) (i) and (ii) only
(D) (ii) and (iii) only


Answer: (B)

Explanation: In Boolean algebra, x<y and y<z, then x<y is true but x=y is false.

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