#gateappliedcourse

Question

Let A={x,y,z}. The number of relations containing (x,y) and (x,z) which are reflexive and symmetric but not transitive is?

Comments

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Answer 1

Answer : 1

The number of relations containing $(x,y)$ and $(x,z)$ which are reflexive, symmetric, but not transitive is $1$.

$ \{(x,y), (y,x), (x,z), (z,x), (x,x), (y,y), (z,z)\}$

In all three of these relations, $(x,y)$ and $(x,z)$ are present, and the relation is reflexive because it contains $(x,x)$, $(y,y)$, and $(z,z)$. However, the relation is not transitive because it does not contain $(y,z)$.

Comments

This relation is Transitive.

$x$ $\mathbb{R}$ $y$ and $y$ $\mathbb{R}$ $x$  $\Rightarrow$ $x$ $\mathbb{R}$ $x$ , and $(x,x)$ $\epsilon$ $\mathbb{R}$.

So, this relation is always transitive.

 

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@Sahil5635

the above given relation is not transitive (z,x )(x,y)=>(z,y ) not belongs to relation

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Yes, you are correct, I forgot to consider this transitive edge.

thanks:)