Draw the digraph and find matrix of relation for R∪ 𝑆 and R∩ 𝑆 if relations R & Sare defined on a set 𝐴 = {1,2,3,4,5,6} as𝑅 = {(𝑎, 𝑏) 𝑠𝑢𝑐ℎ𝑡ℎ𝑎𝑡 𝑎 𝑑𝑒𝑣𝑖𝑑𝑒𝑠 𝑏, ∀ 𝑎, 𝑏 ∈ 𝐴 }𝑆 = {(𝑎, 𝑏) 𝑠𝑢𝑐ℎ𝑡ℎ𝑎𝑡 𝑎 𝑖𝑠 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 𝑏 , ∀ 𝑎, 𝑏 ∈ 𝐴 }

To draw the digraph for the relations R and S, we need to represent the elements of set A = {1, 2, 3, 4, 5, 6} as nodes in the graph.

For relation R, we have (a, b) such that a divides b for all a, b in A. This means that if a is a divisor of b, there will be a directed edge from node a to node b in the digraph.

Similarly, for relation S, we have (a, b) such that a is a multiple of b for all a, b in A. This means that if a is a multiple of b, there will be a directed edge from node a to node b in the digraph.

To find the matrix of relation R∪S, we need to combine the edges from both R and S. If there is an edge from a to b in either R or S, there will be an edge from a to b in R∪S. We can represent this matrix by marking a 1 in the corresponding position if there is an edge, and a 0 otherwise.

To find the matrix of relation R∩S, we need to find the common edges between R and S. If there is an edge from a to b in both R and S, there will be an edge from a to b in R∩S. Again, we can represent this matrix by marking a 1 in the corresponding position if there is an edge, and a 0 otherwise.

I hope this helps! Let me know if you have any further questions.