Consider the following relation ron a set a r={(a, a) (a, b) (b, a) (b, b) (b, c) (cc) } consider the following statements stat 1: r is an equivalence relation stat 2: r is not an equivalence relation because it is not transitive stat 3: r is not an equivalence relation because it is not symmetric stat 4: adding just one ordered pair to r can make the new relation equivalence relation choose the correct statements a) stat 1 is true and stat 4 is true b) stat 2 is true c)stat 4 is false d) stat 3 is false d)stat 3 is false a) stat 1 is true and stat 4 is true b)stat 2 is true

Answer with Step-by-step explanation:

We are given that a relation on set A

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

We have to tell which statement is true about the given relation.

We know that if relations is reflexive, symmetric and transitive then the relation is called equivalence relation.

Reflexive:if (a,a) is present in the given relation for every element a belongs to A.

Symmetric :If (a,b) are present in the relation the  (b,a) is also present in the given relation for every ordered pair (a,b) belongs to R.

Transitive: If (a,b) and (b,c) are present in the given relation then (c,a) is also present in the given relation.

Therefore, given relation is reflexive .

Given relation is not symmetric and not transitive because (c,b) and (c,a) are not present in the given relation.Therefore, relation is not equivalence.

Therefore,

Option

(a) Stat 2 : true .

(c) Stat 4: False Because we need two ordered pair to make the equivalence relation.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

w< 4

step-by-step explanation: