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.