Discrete Mathematic Question

Raza

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

[tex]p \rightarrow q \vee r[/tex]

[tex]p \wedge \neg q \rightarrow r [/tex]

[tex]p \wedge \neg r \rightarrow q[/tex]


2. Relevant equations
[tex]p \rightarrow q \equiv \neg p \wedge q[/tex]

3. The attempt at a solution

[tex]p \rightarrow q \vee r[/tex]

[tex]p \rightarrow \neg q \rightarrow r[/tex]

[tex]\neg p \wedge \neg q \rightarrow r[/tex]

That's all I got. Please help me.

HallsofIvy

I'm not sure what you are doing. I don't see how you got [itex]p \rightarrow \neg q \wedge r[/itex] from any of those!

Using your "relevant equation", the first becomes [itex]\not p\wedge (q\vee r)[/itex], the second [itex]\not (p\wedge \not q)\vee r[/itex] which is itself equivalent ot [itex](\not p \vee q)\vee r.

Frankly I would use truth tables!

Raza

I had made a mistake, now I have corrected it. and I am not allowed to use the truth table.

Thank you

Raza

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

[tex]=0.079984804cm^3[/tex]

[tex]=0.08cm^3[/tex]

Raza

Again, please ignore this
just ignore this, I need latex for MS word.
[tex]\frac{\Delta v}{v} = \sqrt{(\frac{\Delta \ell}{\ell})^2 + (\frac{\Delta t}{t})^2}[/tex]

[tex]\frac{\Delta v}{v} = \sqrt{(\frac{0.001}{0.101})^2 + (\frac{0.00001}{0.3950})^2}[/tex]

[tex]\frac{\Delta v}{v} = 0.0099m/s[/tex]

[tex]\frac{\Delta a}{a} = \sqrt{(\frac{\Delta v_1}{v_1})^2 + (\frac{\Delta v_2}{v_2})^2} + (\frac{\Delta d}{d})^2}[/tex]

[tex]\frac{\Delta a}{a} = \sqrt{(\frac{0.0099}{0.256})^2 + (\frac{0.0099}{0.620})^2 + (\frac{0.01}{0.60})^2}[/tex]

[tex]\frac{\Delta a}{a} = \sqrt{(0.00149) + (0.000254) + (0.000277)}[/tex]

[tex]\frac{\Delta a}{a} = \sqrt{0.002021}[/tex]

[tex]\frac{\Delta a}{a} = 0.041945[/tex]

[tex]\frac{\Delta a}{a} = 0.042 m/s^2[/tex]