3.2 Totuustauluthttps://peda.net/id/2f7d72084a32019-03-19T14:04:45+02:00https://peda.net/:static/535/peda.net.logo.bg.svg<div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div>
342https://peda.net/id/02365ae04fc2019-03-26T14:09:30+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26P%26%5Cleft(A%5Cwedge%20B%5Cright)%5Cvee%5Cleft(%5Cneg%20A%5Cwedge%5Cneg%20B%5Cright)%5C%5C%0A%5Chline%0A1%261%261%261%5C%5C%0A1%260%260%260%5C%5C%0A0%261%260%260%5C%5C%0A0%260%261%261%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&P&\left(A\wedge B\right)\vee\left(\neg A\wedge\neg B\right)\\ \hline 1&1&1&1\\ 1&0&0&0\\ 0&1&0&0\\ 0&0&1&1 \end{array}"/></div>
2019-03-26T14:09:30+02:00337https://peda.net/id/954a42024fb2019-03-26T14:06:27+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26%5Cneg%5Cleft(%5Cneg%20A%5Cwedge%5Cneg%20B%5Cright)%26%5Cneg%5Cleft(%5Cneg%20A%5Cvee%5Cneg%20B%5Cright)%26A%5Cwedge%20B%5C%5C%0A%5Chline%0A1%261%261%261%261%5C%5C%0A1%260%261%260%260%5C%5C%0A0%261%261%260%260%5C%5C%0A0%260%260%260%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&\neg\left(\neg A\wedge\neg B\right)&\neg\left(\neg A\vee\neg B\right)&A\wedge B\\ \hline 1&1&1&1&1\\ 1&0&1&0&0\\ 0&1&1&0&0\\ 0&0&0&0&0 \end{array}"/><br/>
<br/>
jälkimmäinen lause on ekvivalentti </div>
2019-03-26T14:06:27+02:00336https://peda.net/id/06b11ef84fb2019-03-26T14:02:28+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26%5Cneg%20A%5CRightarrow%5Cneg%20B%26%5Cneg%5Cleft(%5Cneg%20A%5Cwedge%20B%5Cright)%5C%5C%0A%5Chline%0A1%261%260%260%5C%5C%0A1%260%261%261%5C%5C%0A0%261%260%260%5C%5C%0A0%260%261%261%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&\neg A\Rightarrow\neg B&\neg\left(\neg A\wedge B\right)\\ \hline 1&1&0&0\\ 1&0&1&1\\ 0&1&0&0\\ 0&0&1&1 \end{array}"/><br/>
lauseet on ekvivalentit</div>
2019-03-26T14:02:28+02:00334https://peda.net/id/8b69fdbe4fb2019-03-26T13:59:01+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26%5Cleft(A%5CLeftrightarrow%20B%5Cright)%5Cvee%5Cleft(%5Cneg%20A%5CRightarrow%20B%5Cright)%5C%5C%0A%5Chline%0A1%261%261%5C%5C%0A1%260%260%5C%5C%0A0%261%261%5C%5C%0A0%260%261%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&\left(A\Leftrightarrow B\right)\vee\left(\neg A\Rightarrow B\right)\\ \hline 1&1&1\\ 1&0&0\\ 0&1&1\\ 0&0&1 \end{array}"/><br/>
<br/>
</div>
2019-03-26T13:59:01+02:00331https://peda.net/id/c7ab75ec4fb2019-03-26T13:53:32+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AP%26S%26%5Cneg%5Cleft(P%5CRightarrow%20S%5Cright)%26%5Cneg%20P%5CRightarrow%5Cneg%20S%26P%5Cwedge%5Cneg%20S%5C%5C%0A%5Chline%0A1%261%260%261%260%5C%5C%0A1%260%261%261%261%5C%5C%0A0%261%260%260%260%5C%5C%0A0%260%260%261%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} P&S&\neg\left(P\Rightarrow S\right)&\neg P\Rightarrow\neg S&P\wedge\neg S\\ \hline 1&1&0&1&0\\ 1&0&1&1&1\\ 0&1&0&0&0\\ 0&0&0&1&0 \end{array}"/><br/>
<br/>
<br/>
hilma on oikeassa</div>
2019-03-26T13:53:32+02:00329https://peda.net/id/f6c2e60e4fb2019-03-26T13:47:42+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26%5Cleft(A%5CRightarrow%20B%5Cright)%5Cvee%20B%5C%5C%0A%5Chline%0A1%261%261%5C%5C%0A1%260%260%5C%5C%0A0%261%261%5C%5C%0A0%260%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&\left(A\Rightarrow B\right)\vee B\\ \hline 1&1&1\\ 1&0&0\\ 0&1&1\\ 0&0&0 \end{array}"/></div>
<div>lause on tosi kun B on tosi</div>
2019-03-26T13:47:42+02:00328https://peda.net/id/928de3644fb2019-03-26T13:44:54+02:00<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26A%5Cwedge%20B%26A%5Cvee%20B%26%5Cneg%20A%5Cvee%20B%26A%5Cwedge%5Cneg%20B%5C%5C%0A%5Chline%0A0%261%260%261%261%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&A\wedge B&A\vee B&\neg A\vee B&A\wedge\neg B\\ \hline 0&1&0&1&1&0 \end{array}"/></div>
<div> </div>
2019-03-26T13:44:54+02:00333https://peda.net/id/0c7ed9d44fb2019-03-26T13:19:40+02:00a) menen kalaan jos on lauantai ja en mene kalaan jos ei ole hyvä sää<br/>
b)<br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0AA%26B%26C%26%5Cneg%20C%26%5Cleft(A%5CRightarrow%20B%5Cright)%5Cwedge%5Cleft(%5Cneg%20C%5CRightarrow%5Cneg%20B%5Cright)%5C%5C%0A%5Chline%0A1%261%261%260%261%5C%5C%0A1%261%260%261%260%5C%5C%0A1%260%261%260%260%5C%5C%0A1%260%260%261%260%5C%5C%0A0%261%261%260%260%5C%5C%0A0%261%260%261%260%5C%5C%0A0%260%261%260%260%5C%5C%0A0%260%260%261%260%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} A&B&C&\neg C&\left(A\Rightarrow B\right)\wedge\left(\neg C\Rightarrow\neg B\right)\\ \hline 1&1&1&0&1\\ 1&1&0&1&0\\ 1&0&1&0&0\\ 1&0&0&1&0\\ 0&1&1&0&0\\ 0&1&0&1&0\\ 0&0&1&0&0\\ 0&0&0&1&0 \end{array}"/>2019-03-26T13:19:40+02:00347https://peda.net/id/103ad7464fb2019-03-26T13:05:28+02:00a) ei, koska C on myös vaihtoehto<br/>
b) joo, koska jos mikään lauseista ei ole tosi, silloin \neg B on tosi, väitelause on siis aina tosi2019-03-26T13:05:28+02:00339https://peda.net/id/4ef29b684ca2019-03-22T15:27:58+02:00Hannu menee bileisiin2019-03-22T15:27:58+02:00