Answer to Question #199741 in Discrete Mathematics for Ryan

Question

Consider the following relation on set B = {a, b, {a}, {b}, {a, b}}: P = {(a, b), (b, {a, b}), ({a, b}, a), ({b}, a), (a, {a})}. 

Which one of the following alternatives represents the range of P (ran(P))?

1. {a, b, {a}, {a, b}}

2. {a, b, {a}, {b}, {a, b}}

3. {a, b, {b}, {a, b}}

4. {a, b, {a, b}}

Answer 1

Solution:

Given, P = {(a, b), (b, {a, b}), ({a, b}, a), ({b}, a), (a, {a})}. 

For any set A = {(x,y)}, range of A = {y}

So, ran(P)=range of P = {b,{a,b},a,{a}} = {a, b, {a}, {a, b}}

Hence, option 1 is correct.