## Discrete Mathematic Question

1. The problem statement, all variables and given/known data
Hi. I need to prove that these 3 eqns are the same.

$$p \rightarrow q \vee r$$

$$p \wedge \neg q \rightarrow r$$

$$p \wedge \neg r \rightarrow q$$

2. Relevant equations
$$p \rightarrow q \equiv \neg p \wedge q$$

3. The attempt at a solution

$$p \rightarrow q \vee r$$

$$p \rightarrow \neg q \rightarrow r$$

$$\neg p \wedge \neg q \rightarrow r$$

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 Recognitions: Gold Member Science Advisor Staff Emeritus I'm not sure what you are doing. I don't see how you got $p \rightarrow \neg q \wedge r$ from any of those! Using your "relevant equation", the first becomes $\not p\wedge (q\vee r)$, the second $\not (p\wedge \not q)\vee r$ which is itself equivalent ot [itex](\not p \vee q)\vee r. Frankly I would use truth tables!
 I had made a mistake, now I have corrected it. and I am not allowed to use the truth table. Thank you

## Discrete Mathematic Question

just ignore this, I need latex for MS word.
$$\sqrt{2 \times (\frac{0.1}{3.2})^2 + (\frac{0.2}{3.0})^2}$$

$$=0.079984804cm^3$$

$$=0.08cm^3$$

 Again, please ignore this just ignore this, I need latex for MS word. $$\frac{\Delta v}{v} = \sqrt{(\frac{\Delta \ell}{\ell})^2 + (\frac{\Delta t}{t})^2}$$ $$\frac{\Delta v}{v} = \sqrt{(\frac{0.001}{0.101})^2 + (\frac{0.00001}{0.3950})^2}$$ $$\frac{\Delta v}{v} = 0.0099m/s$$ $$\frac{\Delta a}{a} = \sqrt{(\frac{\Delta v_1}{v_1})^2 + (\frac{\Delta v_2}{v_2})^2} + (\frac{\Delta d}{d})^2}$$ $$\frac{\Delta a}{a} = \sqrt{(\frac{0.0099}{0.256})^2 + (\frac{0.0099}{0.620})^2 + (\frac{0.01}{0.60})^2}$$ $$\frac{\Delta a}{a} = \sqrt{(0.00149) + (0.000254) + (0.000277)}$$ $$\frac{\Delta a}{a} = \sqrt{0.002021}$$ $$\frac{\Delta a}{a} = 0.041945$$ $$\frac{\Delta a}{a} = 0.042 m/s^2$$