A = {0, 1, 2, 3, 4, 5, 6, 7} ,suppose R and T are Two relations on A such that R = {(x, y) : 2 * x + 3y = 15} ,T= {(x,y):3x+2y in A} Write down R,T and R°T as a set of ordered pairs?

First, let's find the set of ordered pairs for R and T.

R = {(x, y) : 2x + 3y = 15}

For R, we need to find the pairs (x, y) that satisfy the equation 2x + 3y = 15. However, since x and y must be in the set A = {0, 1, 2, 3, 4, 5, 6, 7}, the only pairs that satisfy this equation are (0,5), (3,3), and (5,1). So,

R = {(0,5), (3,3), (5,1)}

Now, let's find T.

T = {(x, y) : 3x + 2y ∈ A}

For T, we need to find the pairs (x, y) that satisfy the equation 3x + 2y ∈ A. This means that 3x + 2y should be an element of the set A. The pairs that satisfy this equation are (0,0), (0,1), (0,2), (0,3), (1,0), (1,2), (2,1), (2,3), (3,0), (3,2), (4,1), and (4,3). So,

T = {(0,0), (0,1), (0,2), (0,3), (1,0), (1,2), (2,1), (2,3), (3,0), (3,2), (4,1), (4,3)}

Finally, let's find R°T.

R°T = {(x, z) : ∃y, (x, y) ∈ R and (y, z) ∈ T}

For R°T, we need to find the pairs (x, z) such that there exists a y which is related to x in R and to z in T. This means that we need to find a common y in the pairs of R and T. The pairs that satisfy this condition are (0,0), (0,1), (0,2), (0,3), (3,0), and (3,2). So,

R°T = {(0,0), (0,1), (0,2), (0,3), (3,0), (3,2)}