Mathematics, 12.07.2019 23:40 alexdziob01
Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ and mr2 = ⎡ ⎣ 0 1 0 0 1 1 1 1 1 ⎤ ⎦. find the matrices that represent a. r1 ∪ r2. b. r1 ∩ r2. c. r2 ◦r1. d. r1 ◦r1. e. r1 ⊕ r2.
Answers: 1
![r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \,\, and \,\, r2= \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right]](/tpl/images/0082/7278/42097.png)
![r1 \cup r2 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&1&1\end{array}\right]](/tpl/images/0082/7278/7b95c.png)
![r1 \cap r2 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&0&0\end{array}\right]](/tpl/images/0082/7278/a921c.png)
![r2 \circ r1 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&1&1\\2&2&1\end{array}\right]](/tpl/images/0082/7278/80cf0.png)
![r1 \circ r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&2&1\\0&1&0\end{array}\right]](/tpl/images/0082/7278/6c0b5.png)
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Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ an...
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