Is it possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive

Step-by-step explanation:

Let

Set A={a,b,c}

Now, define a relation R on set A is given by

R={(a,a),(a,b),(b,a),(b,b)}

For reflexive

A relation is called reflexive if (a,a) for every element a

Therefore, the relation R is  not reflexive.

For symmetric

If then

We have

and

Hence, R is symmetric.

For transitive

If (a,b) and (b,c) then (a,c)

Here,

and

and

Therefore, R is transitive.

Yes, it is possible to have  a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

y > 1/3x

y < = -x + 4

hope this : )