Represent each of these relations on {1, 2, 3, 4} with a matrix (with the elements of this set listed in increasing order). a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)} c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)} d) {(2, 4), (3, 1), (3, 2), (3, 4)}

for a  a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

Step-by-step explanation:

in matrix, arrays are placed in rows , which represents the horizontal sides from left to right, while arrays in the column are placed vertically from top to bottom. Here, we placed the arrays in a 4x4 matrix

for a  a) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}

for b

b) {(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}

for c) {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

for d d) {(2, 4), (3, 1), (3, 2), (3, 4)}

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: