Please Solve this question of Discrete mathematics

Let D and S be relations on A = {0, 1, 2, 3}.

• D = {(a, b) | b = (3a+1) mod 4}

• S = {(a, b) | b < a+1}

• D = {(0, 4), (1, 16), (2, 28), (3, 40)}

• S = {(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3)}

S_{°}D =???????????

Then find values of S_{°}D by writing all the intermediate steps

Re: Please Solve this question of Discrete mathematics

have you made any effort at it yet?

Re: Please Solve this question of Discrete mathematics

Either your first two definitions for D and S are wrong or the second two are. My guess is the second two are. Note: If $\displaystyle D = \{(0,4),(1,16),(2,28),(3,40)\}$, then $\displaystyle D \not \subset A\times A$, so it is not a relation on $\displaystyle A$

Based on the first definition, $\displaystyle D = \{(0,1), (1,0), (2,3), (3,2)\}$

Similarly, the $\displaystyle S$ you gave does not match the definition you gave, nor is it even a relation on $\displaystyle A$. Using the first definition,

$\displaystyle S = \{(0,0),(1,0),(1,1),(2,0),(2,1),(2,2),(3,0),(3,1), (3,2),(3,3)\}$

Next, use the definition for composition of binary relations.

Re: Please Solve this question of Discrete mathematics

Dear sir Bundle of thanks for guiding me. After posting my question I realized that I solved D and S were really wrong. Sir my question is still incomplete because I want to find S°D =???????????

Re: Please Solve this question of Discrete mathematics

I find S°D={(0,0),(0,1),(1,0),(2,0),(2,1),(2,2),(2,3),(3, 0),(3,1),(3,2)}. is am I correct????? or Not. If not then please find S°D=????????????

Re: Please Solve this question of Discrete mathematics

Quote:

Originally Posted by

**ahsanalisony** Let D and S be relations on A = {0, 1, 2, 3}.

• D = {(a, b) | b = (3a+1) mod 4}

• S = {(a, b) | b < a+1}

$S\circ D =?$

First the set $A$ has only four elements. Therefore, any relation can have at most sixteen pairs.

To do this question you must know what relations look like:

$D=\{(0,1)~,(1,0)~,(2,3)~,(3,2)\}$ and

$S=\{(0,0)~,(1,0)~,(1,1)~,(2,0)~,(2,1)~,(2,2)~,(3, 0)~,(3,1)~,(3,2)~,(3,3)\}$

Now, try again!

Re: Please Solve this question of Discrete mathematics

To calculate $\displaystyle S\circ D$, take all of the pairs of $\displaystyle S$ and pairs of $\displaystyle D$ where the second coordinate from the pair in $\displaystyle S$ is the same as the first coordinate of the pair in $\displaystyle D$ and group them together:

Pairs in $\displaystyle S$ where the second coordinate is zero:

$\displaystyle (0,0), (1,0), (2,0), (3,0)$

Pairs in $\displaystyle D$ where the first coordinate is zero:

$\displaystyle (0,1)$

Each pair from $\displaystyle S$ and that single pair from $\displaystyle D$ form pairs in $\displaystyle S\circ D$:

$\displaystyle (0,1), (1,1), (2,1), (3,1)$

(That is the first coordinate from the pair in $\displaystyle S$ and the second coordinate from the pair in $\displaystyle D$)

Now, do the same for pairs in $\displaystyle S$ where the second coordinate is one and pairs in $\displaystyle D$ where the first coordinate is one. Then move on to when they are both two, and finally when they are both three. That will give you all elements of $\displaystyle S\circ D$.