UGC NET CSE | December 2018 | Part 2 | Question: 6

Question

The relation $\leq$ and $>$ on a boolean algebra are defined as:

$x \leq y$ if and only if $x \vee y =y$

$x <y$ means $x \leq y$ but $x \neq y$

$x \geq y$ means $y \leq x$ and

$x>y$ means $y<x$

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

1. If $x \leq y$ and $y \leq z$, then $x \leq z$
2. If $x \leq y$ and $y \leq x$, then $x = y$
3. If $x < y$ and $y < z$, then $x \leq y$
4. If $x < y$ and $y <  z$, then $x < y$

Choose the correct answer from the code given below:

• A. i and ii only
• B. ii and iii only
• C. iii only
• D. iv only

Comments

option 3  rest are true

Answer 1

In Boolean algebra

x<y and y<z, then x<y is true but x=y is false.

Answer is option 3.