Representation of two relation matrices

[Panphobia]

Homework Statement

The Attempt at a Solution

I know what relations are individually but what do I do to represent the composition of both? Is it some matrix operation? Would I multiply them, but instead of adding I use the boolean sum?

 

[STEMucator]

Homework Statement

The Attempt at a Solution

I know what relations are individually but what do I do to represent the composition of both? Is it some matrix operation?

Let ##R = R_1 \circ R_2 : A → C##

If you have an element ##a \in A##, how would you be mapping it all the way to ##C## given the two matrices you have?

Hint: Think about the dimensions of the elements in ##A##.

 

[Panphobia]

I know that I can use the venn diagrams and draw arrows and stuff, but when I multiply the two matrices together, I get the right answer. So will it work for all of them?

 

[STEMucator]

I know that I can use the venn diagrams and draw arrows and stuff, but when I multiply the two matrices together, I get the right answer. So will it work for all of them?

Yes, suppose you denote the upper matrix in the problem by ##M_1## and the lower one by ##M_2##.

According to ##R_1##, you map the elements of ##A## to ##B##. The matrix of the relation happens to be ##M_1##.

So ##aM_1 \in B##.

Then to get to ##C##, you multiply by ##M_2##.

So ##aM_1M_2 \in C##.

 

[Panphobia]

Ahh alright, and I was right to assume that you used the boolean sum, during the multiplicative process?

 

[STEMucator]

I believe the question is simply asking you to multiply ##M_1## and ##M_2##. I'm not quite sure what you mean by 'Boolean sum' though.

 

[Panphobia]

If an element of A, a, and an element of B, b, are related then, aRb == 1, so there can only be values of 0 or 1, boolean sum is defined as a logical or so
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1

 

[STEMucator]

If an element of A, a, and an element of B, b, are related then, aRb == 1, so there can only be values of 0 or 1, boolean sum is defined as a logical or so
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1

Ahh you intended these as logical matrices. If that's the case then yes.