Question

1. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find a. R1 ∪ R2 b. R1 ∩ R2 c. R1 – R2 d. R2 – R1

Answer 1

Answer:

a) R1 ∪ R2={(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

b)  R1 ∩ R2= {(1, 2), (2, 3), (3, 4)}

c) R1 – R2= ∅

d) R2 – R1= {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}

Step-by-step explanation:

We know that:

R1 = {(1, 2), (2, 3), (3, 4)}

R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

Therefore, we get  

a) R1 ∪ R2={(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

b)  R1 ∩ R2= {(1, 2), (2, 3), (3, 4)}

c) R1 – R2= ∅

d) R2 – R1= {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}